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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{6}=b^{6}=c^{6}=[b,c]=1, b^{a}=b^{5}, c^{a}=c^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_6^2:C_6$ 1A $1$ $1$ $C_6^2:C_6$ 1A 1A $1$
$C_6^2:C_6$ 2A $2$ $1$ $C_6^2:C_6$ 1A 2A $c^{3}$
$C_6^2:C_6$ 2B $2$ $1$ $C_6^2:C_6$ 1A 2B $b^{3}$
$C_6^2:C_6$ 2C $2$ $1$ $C_6^2:C_6$ 1A 2C $b^{3}c^{3}$
$C_6^2:C_6$ 2D $2$ $9$ $C_2^2\times C_6$ 1A 2D $a^{3}$
$C_6^2:C_6$ 2E $2$ $9$ $C_2^2\times C_6$ 1A 2E $a^{3}c$
$C_6^2:C_6$ 2F $2$ $9$ $C_2^2\times C_6$ 1A 2F $a^{3}b$
$C_6^2:C_6$ 2G $2$ $9$ $C_2^2\times C_6$ 1A 2G $a^{3}bc$
$C_6^2:C_6$ 3A1 $3$ $1$ $C_6^2:C_6$ 3A-1 1A $a^{4}$
$C_6^2:C_6$ 3A-1 $3$ $1$ $C_6^2:C_6$ 3A1 1A $a^{2}$
$C_6^2:C_6$ 3B $3$ $2$ $C_3\times C_6^2$ 3B 1A $c^{2}$
$C_6^2:C_6$ 3C $3$ $2$ $C_3\times C_6^2$ 3C 1A $b^{2}$
$C_6^2:C_6$ 3D $3$ $2$ $C_3\times C_6^2$ 3D 1A $b^{4}c^{2}$
$C_6^2:C_6$ 3E $3$ $2$ $C_3\times C_6^2$ 3E 1A $b^{2}c^{2}$
$C_6^2:C_6$ 3F1 $3$ $2$ $C_3\times C_6^2$ 3F-1 1A $a^{4}c^{2}$
$C_6^2:C_6$ 3F-1 $3$ $2$ $C_3\times C_6^2$ 3F1 1A $a^{2}c^{4}$
$C_6^2:C_6$ 3G1 $3$ $2$ $C_3\times C_6^2$ 3G-1 1A $a^{4}b^{2}$
$C_6^2:C_6$ 3G-1 $3$ $2$ $C_3\times C_6^2$ 3G1 1A $a^{2}b^{4}$
$C_6^2:C_6$ 3H1 $3$ $2$ $C_3\times C_6^2$ 3H-1 1A $a^{4}b^{4}c^{2}$
$C_6^2:C_6$ 3H-1 $3$ $2$ $C_3\times C_6^2$ 3H1 1A $a^{2}b^{2}c^{4}$
$C_6^2:C_6$ 3I1 $3$ $2$ $C_3\times C_6^2$ 3I-1 1A $a^{4}b^{2}c^{2}$
$C_6^2:C_6$ 3I-1 $3$ $2$ $C_3\times C_6^2$ 3I1 1A $a^{2}b^{4}c^{4}$
$C_6^2:C_6$ 6A1 $6$ $1$ $C_6^2:C_6$ 3A1 2A $a^{2}c^{3}$
$C_6^2:C_6$ 6A-1 $6$ $1$ $C_6^2:C_6$ 3A-1 2A $a^{4}c^{3}$
$C_6^2:C_6$ 6B1 $6$ $1$ $C_6^2:C_6$ 3A1 2B $a^{2}b^{3}$
$C_6^2:C_6$ 6B-1 $6$ $1$ $C_6^2:C_6$ 3A-1 2B $a^{4}b^{3}$
$C_6^2:C_6$ 6C1 $6$ $1$ $C_6^2:C_6$ 3A1 2C $a^{2}b^{3}c^{3}$
$C_6^2:C_6$ 6C-1 $6$ $1$ $C_6^2:C_6$ 3A-1 2C $a^{4}b^{3}c^{3}$
$C_6^2:C_6$ 6D $6$ $2$ $C_3\times C_6^2$ 3B 2A $c$
$C_6^2:C_6$ 6E $6$ $2$ $C_3\times C_6^2$ 3C 2B $b$
$C_6^2:C_6$ 6F $6$ $2$ $C_3\times C_6^2$ 3D 2A $b^{2}c$
$C_6^2:C_6$ 6G $6$ $2$ $C_3\times C_6^2$ 3D 2B $bc^{2}$
$C_6^2:C_6$ 6H $6$ $2$ $C_3\times C_6^2$ 3E 2C $bc$
$C_6^2:C_6$ 6I $6$ $2$ $C_3\times C_6^2$ 3E 2A $b^{4}c$
$C_6^2:C_6$ 6J $6$ $2$ $C_3\times C_6^2$ 3E 2B $bc^{4}$
$C_6^2:C_6$ 6K $6$ $2$ $C_3\times C_6^2$ 3C 2A $b^{2}c^{3}$
$C_6^2:C_6$ 6L $6$ $2$ $C_3\times C_6^2$ 3C 2C $bc^{3}$
$C_6^2:C_6$ 6M $6$ $2$ $C_3\times C_6^2$ 3B 2B $b^{3}c^{2}$
$C_6^2:C_6$ 6N $6$ $2$ $C_3\times C_6^2$ 3B 2C $b^{3}c$
$C_6^2:C_6$ 6O $6$ $2$ $C_3\times C_6^2$ 3D 2C $bc^{5}$
$C_6^2:C_6$ 6P1 $6$ $2$ $C_3\times C_6^2$ 3F1 2A $a^{2}c$
$C_6^2:C_6$ 6P-1 $6$ $2$ $C_3\times C_6^2$ 3F-1 2A $a^{4}c$
$C_6^2:C_6$ 6Q1 $6$ $2$ $C_3\times C_6^2$ 3G1 2B $a^{2}b$
$C_6^2:C_6$ 6Q-1 $6$ $2$ $C_3\times C_6^2$ 3G-1 2B $a^{4}b$
$C_6^2:C_6$ 6R1 $6$ $2$ $C_3\times C_6^2$ 3H1 2A $a^{2}b^{2}c$
$C_6^2:C_6$ 6R-1 $6$ $2$ $C_3\times C_6^2$ 3H-1 2A $a^{4}b^{2}c$
$C_6^2:C_6$ 6S1 $6$ $2$ $C_3\times C_6^2$ 3H1 2B $a^{2}bc^{2}$
$C_6^2:C_6$ 6S-1 $6$ $2$ $C_3\times C_6^2$ 3H-1 2B $a^{4}bc^{2}$
$C_6^2:C_6$ 6T1 $6$ $2$ $C_3\times C_6^2$ 3I1 2C $a^{2}bc$
$C_6^2:C_6$ 6T-1 $6$ $2$ $C_3\times C_6^2$ 3I-1 2C $a^{4}bc$
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