Commutative semigroups of size 4

<structure name="CSgrp_4_1" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  0  0  </row>
    <row id="3">  0  0  0  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_2" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  0  0  </row>
    <row id="3">  0  0  0  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_3" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  0  0  </row>
    <row id="3">  0  0  0  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_4" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  0  1  </row>
    <row id="3">  0  0  1  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_5" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  0  1  </row>
    <row id="3">  0  0  1  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_6" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  0  1  </row>
    <row id="3">  0  0  1  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_7" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  0  2  </row>
    <row id="3">  0  0  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_8" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  1  0  </row>
    <row id="3">  0  0  0  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_9" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  1  0  </row>
    <row id="3">  0  0  0  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_10" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  1  1  </row>
    <row id="3">  0  0  1  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_11" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  2  0  </row>
    <row id="3">  0  0  0  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_12" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  2  2  </row>
    <row id="3">  0  0  2  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_13" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  2  2  </row>
    <row id="3">  0  0  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_14" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  0  </row>
    <row id="2">  0  0  2  3  </row>
    <row id="3">  0  0  3  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_15" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  1  </row>
    <row id="2">  0  0  0  1  </row>
    <row id="3">  0  1  1  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_16" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  1  </row>
    <row id="2">  0  0  0  2  </row>
    <row id="3">  0  1  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_17" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  1  </row>
    <row id="2">  0  0  1  2  </row>
    <row id="3">  0  1  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_18" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  1  </row>
    <row id="2">  0  0  2  0  </row>
    <row id="3">  0  1  0  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_19" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  0  1  </row>
    <row id="2">  0  0  2  2  </row>
    <row id="3">  0  1  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_20" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  1  1  </row>
    <row id="2">  0  1  2  2  </row>
    <row id="3">  0  1  2  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_21" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  1  1  </row>
    <row id="2">  0  1  2  2  </row>
    <row id="3">  0  1  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_22" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  0  1  1  </row>
    <row id="2">  0  1  2  3  </row>
    <row id="3">  0  1  3  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_23" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  0  0  </row>
    <row id="2">  0  0  2  0  </row>
    <row id="3">  0  0  0  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_24" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  0  0  </row>
    <row id="2">  0  0  2  2  </row>
    <row id="3">  0  0  2  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_25" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  0  0  </row>
    <row id="2">  0  0  2  2  </row>
    <row id="3">  0  0  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_26" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  0  0  </row>
    <row id="2">  0  0  2  3  </row>
    <row id="3">  0  0  3  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_27" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  0  1  </row>
    <row id="2">  0  0  2  2  </row>
    <row id="3">  0  1  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_28" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  1  1  </row>
    <row id="3">  0  1  1  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_29" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  1  1  </row>
    <row id="3">  0  1  1  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_30" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  1  1  </row>
    <row id="3">  0  1  1  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_31" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  1  2  </row>
    <row id="3">  0  1  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_32" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  2  1  </row>
    <row id="3">  0  1  1  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_33" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  2  2  </row>
    <row id="3">  0  1  2  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_34" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  2  2  </row>
    <row id="3">  0  1  2  3  </row>
  </operation>
</structure>

<structure name="CSgrp_4_35" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  1  </row>
    <row id="2">  0  1  2  3  </row>
    <row id="3">  0  1  3  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_36" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  3  </row>
    <row id="2">  0  1  1  3  </row>
    <row id="3">  0  3  3  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_37" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  1  3  </row>
    <row id="2">  0  1  2  3  </row>
    <row id="3">  0  3  3  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_38" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  2  2  </row>
    <row id="2">  0  2  1  1  </row>
    <row id="3">  0  2  1  1  </row>
  </operation>
</structure>

<structure name="CSgrp_4_39" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  0  </row>
    <row id="1">  0  1  2  3  </row>
    <row id="2">  0  2  3  1  </row>
    <row id="3">  0  3  1  2  </row>
  </operation>
</structure>

<structure name="CSgrp_4_40" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  0  0  3  </row>
    <row id="2">  0  0  0  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_41" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  0  0  3  </row>
    <row id="2">  0  0  1  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_42" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  0  0  3  </row>
    <row id="2">  0  0  2  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_43" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  0  1  3  </row>
    <row id="2">  0  1  2  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_44" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  1  0  3  </row>
    <row id="2">  0  0  2  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_45" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  1  1  3  </row>
    <row id="2">  0  1  1  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_46" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  1  1  3  </row>
    <row id="2">  0  1  2  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_47" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  0  3  </row>
    <row id="1">  0  1  2  3  </row>
    <row id="2">  0  2  1  3  </row>
    <row id="3">  3  3  3  0  </row>
  </operation>
</structure>

<structure name="CSgrp_4_48" size="4">
  <element id="0"/>
  <element id="1"/>
  <element id="2"/>
  <element id="3"/>
  <operation name="product" symbol="\cdot" arity="2" type="table">
    <row id="0">  0  0  2  2  </row>
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