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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{6}=c^{132}=[a,b]=[b,c]=1, c^{a}=b^{3}c^{65} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 11P
$D_{66}:C_{12}$ 1A $1$ $1$ $D_{66}:C_{12}$ 1A 1A 1A $1$
$D_{66}:C_{12}$ 2A $2$ $1$ $D_{66}:C_{12}$ 1A 2A 2A $b^{3}$
$D_{66}:C_{12}$ 2B $2$ $1$ $D_{66}:C_{12}$ 1A 2B 2B $b^{3}c^{66}$
$D_{66}:C_{12}$ 2C $2$ $1$ $D_{66}:C_{12}$ 1A 2C 2C $c^{66}$
$D_{66}:C_{12}$ 2D $2$ $66$ $C_2^2\times C_6$ 1A 2D 2D $a$
$D_{66}:C_{12}$ 2E $2$ $66$ $C_2^2\times C_6$ 1A 2E 2E $ac^{66}$
$D_{66}:C_{12}$ 3A1 $3$ $1$ $D_{66}:C_{12}$ 3A-1 1A 3A-1 $b^{4}$
$D_{66}:C_{12}$ 3A-1 $3$ $1$ $D_{66}:C_{12}$ 3A1 1A 3A1 $b^{2}$
$D_{66}:C_{12}$ 3B $3$ $2$ $C_6\times C_{132}$ 3B 1A 3B $c^{88}$
$D_{66}:C_{12}$ 3C1 $3$ $2$ $C_6\times C_{132}$ 3C-1 1A 3C-1 $b^{4}c^{88}$
$D_{66}:C_{12}$ 3C-1 $3$ $2$ $C_6\times C_{132}$ 3C1 1A 3C1 $b^{2}c^{44}$
$D_{66}:C_{12}$ 4A1 $4$ $2$ $C_6\times C_{132}$ 2C 4A-1 4A1 $c^{33}$
$D_{66}:C_{12}$ 4A-1 $4$ $2$ $C_6\times C_{132}$ 2C 4A1 4A-1 $c^{99}$
$D_{66}:C_{12}$ 4B1 $4$ $66$ $C_2\times C_{12}$ 2B 4B-1 4B1 $ac^{111}$
$D_{66}:C_{12}$ 4B-1 $4$ $66$ $C_2\times C_{12}$ 2B 4B1 4B-1 $ab^{3}c^{45}$
$D_{66}:C_{12}$ 6A1 $6$ $1$ $D_{66}:C_{12}$ 3A1 2A 6A-1 $b^{5}$
$D_{66}:C_{12}$ 6A-1 $6$ $1$ $D_{66}:C_{12}$ 3A-1 2A 6A1 $b$
$D_{66}:C_{12}$ 6B1 $6$ $1$ $D_{66}:C_{12}$ 3A1 2B 6B-1 $b^{5}c^{66}$
$D_{66}:C_{12}$ 6B-1 $6$ $1$ $D_{66}:C_{12}$ 3A-1 2B 6B1 $bc^{66}$
$D_{66}:C_{12}$ 6C1 $6$ $1$ $D_{66}:C_{12}$ 3A1 2C 6C-1 $b^{2}c^{66}$
$D_{66}:C_{12}$ 6C-1 $6$ $1$ $D_{66}:C_{12}$ 3A-1 2C 6C1 $b^{4}c^{66}$
$D_{66}:C_{12}$ 6D $6$ $2$ $C_6\times C_{132}$ 3B 2A 6D $b^{3}c^{44}$
$D_{66}:C_{12}$ 6E $6$ $2$ $C_6\times C_{132}$ 3B 2B 6E $b^{3}c^{22}$
$D_{66}:C_{12}$ 6F $6$ $2$ $C_6\times C_{132}$ 3B 2C 6F $c^{22}$
$D_{66}:C_{12}$ 6G1 $6$ $2$ $C_6\times C_{132}$ 3C1 2A 6G-1 $b^{5}c^{44}$
$D_{66}:C_{12}$ 6G-1 $6$ $2$ $C_6\times C_{132}$ 3C-1 2A 6G1 $bc^{88}$
$D_{66}:C_{12}$ 6H1 $6$ $2$ $C_6\times C_{132}$ 3C1 2B 6H-1 $b^{5}c^{22}$
$D_{66}:C_{12}$ 6H-1 $6$ $2$ $C_6\times C_{132}$ 3C-1 2B 6H1 $bc^{110}$
$D_{66}:C_{12}$ 6I1 $6$ $2$ $C_6\times C_{132}$ 3C1 2C 6I-1 $b^{2}c^{22}$
$D_{66}:C_{12}$ 6I-1 $6$ $2$ $C_6\times C_{132}$ 3C-1 2C 6I1 $b^{4}c^{110}$
$D_{66}:C_{12}$ 6J1 $6$ $66$ $C_2^2\times C_6$ 3A1 2D 6J-1 $ab^{2}$
$D_{66}:C_{12}$ 6J-1 $6$ $66$ $C_2^2\times C_6$ 3A-1 2D 6J1 $ab^{4}$
$D_{66}:C_{12}$ 6K1 $6$ $66$ $C_2^2\times C_6$ 3A1 2E 6K-1 $ab^{2}c^{66}$
$D_{66}:C_{12}$ 6K-1 $6$ $66$ $C_2^2\times C_6$ 3A-1 2E 6K1 $ab^{4}c^{66}$
$D_{66}:C_{12}$ 11A1 $11$ $2$ $C_6\times C_{132}$ 11A2 11A3 11A5 $c^{72}$
$D_{66}:C_{12}$ 11A2 $11$ $2$ $C_6\times C_{132}$ 11A4 11A5 11A1 $c^{12}$
$D_{66}:C_{12}$ 11A3 $11$ $2$ $C_6\times C_{132}$ 11A5 11A2 11A4 $c^{84}$
$D_{66}:C_{12}$ 11A4 $11$ $2$ $C_6\times C_{132}$ 11A3 11A1 11A2 $c^{24}$
$D_{66}:C_{12}$ 11A5 $11$ $2$ $C_6\times C_{132}$ 11A1 11A4 11A3 $c^{96}$
$D_{66}:C_{12}$ 12A1 $12$ $2$ $C_6\times C_{132}$ 6F 4A1 12A5 $c^{11}$
$D_{66}:C_{12}$ 12A-1 $12$ $2$ $C_6\times C_{132}$ 6F 4A-1 12A-5 $c^{121}$
$D_{66}:C_{12}$ 12A5 $12$ $2$ $C_6\times C_{132}$ 6F 4A1 12A1 $c^{55}$
$D_{66}:C_{12}$ 12A-5 $12$ $2$ $C_6\times C_{132}$ 6F 4A-1 12A-1 $c^{77}$
$D_{66}:C_{12}$ 12B1 $12$ $2$ $C_6\times C_{132}$ 6I1 4A1 12B5 $b^{4}c^{11}$
$D_{66}:C_{12}$ 12B-1 $12$ $2$ $C_6\times C_{132}$ 6I-1 4A-1 12B-5 $b^{2}c^{121}$
$D_{66}:C_{12}$ 12B5 $12$ $2$ $C_6\times C_{132}$ 6I-1 4A1 12B1 $b^{2}c^{55}$
$D_{66}:C_{12}$ 12B-5 $12$ $2$ $C_6\times C_{132}$ 6I1 4A-1 12B-1 $b^{4}c^{77}$
$D_{66}:C_{12}$ 12C1 $12$ $2$ $C_6\times C_{132}$ 6I-1 4A1 12C5 $b^{2}c^{11}$
$D_{66}:C_{12}$ 12C-1 $12$ $2$ $C_6\times C_{132}$ 6I1 4A-1 12C-5 $b^{4}c^{121}$
$D_{66}:C_{12}$ 12C5 $12$ $2$ $C_6\times C_{132}$ 6I1 4A1 12C1 $b^{4}c^{55}$
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