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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{2}=c^{132}=[a,b]=[b,c]=1, c^{a}=bc^{109} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 11P
$D_{22}:C_{12}$ 1A $1$ $1$ $D_{22}:C_{12}$ 1A 1A 1A $1$
$D_{22}:C_{12}$ 2A $2$ $1$ $D_{22}:C_{12}$ 1A 2A 2A $bc^{66}$
$D_{22}:C_{12}$ 2B $2$ $1$ $D_{22}:C_{12}$ 1A 2B 2B $b$
$D_{22}:C_{12}$ 2C $2$ $1$ $D_{22}:C_{12}$ 1A 2C 2C $c^{66}$
$D_{22}:C_{12}$ 2D $2$ $22$ $C_2^2\times C_6$ 1A 2D 2D $ac^{48}$
$D_{22}:C_{12}$ 2E $2$ $22$ $C_2^2\times C_6$ 1A 2E 2E $ac^{90}$
$D_{22}:C_{12}$ 3A1 $3$ $1$ $D_{22}:C_{12}$ 3A-1 1A 3A-1 $c^{44}$
$D_{22}:C_{12}$ 3A-1 $3$ $1$ $D_{22}:C_{12}$ 3A1 1A 3A1 $c^{88}$
$D_{22}:C_{12}$ 4A1 $4$ $2$ $C_2\times C_{132}$ 2C 4A-1 4A1 $c^{33}$
$D_{22}:C_{12}$ 4A-1 $4$ $2$ $C_2\times C_{132}$ 2C 4A1 4A-1 $c^{99}$
$D_{22}:C_{12}$ 4B1 $4$ $22$ $C_2\times C_{12}$ 2A 4B-1 4B1 $abc^{111}$
$D_{22}:C_{12}$ 4B-1 $4$ $22$ $C_2\times C_{12}$ 2A 4B1 4B-1 $ac^{45}$
$D_{22}:C_{12}$ 6A1 $6$ $1$ $D_{22}:C_{12}$ 3A-1 2A 6A-1 $bc^{110}$
$D_{22}:C_{12}$ 6A-1 $6$ $1$ $D_{22}:C_{12}$ 3A1 2A 6A1 $bc^{22}$
$D_{22}:C_{12}$ 6B1 $6$ $1$ $D_{22}:C_{12}$ 3A-1 2B 6B-1 $bc^{44}$
$D_{22}:C_{12}$ 6B-1 $6$ $1$ $D_{22}:C_{12}$ 3A1 2B 6B1 $bc^{88}$
$D_{22}:C_{12}$ 6C1 $6$ $1$ $D_{22}:C_{12}$ 3A1 2C 6C-1 $c^{22}$
$D_{22}:C_{12}$ 6C-1 $6$ $1$ $D_{22}:C_{12}$ 3A-1 2C 6C1 $c^{110}$
$D_{22}:C_{12}$ 6D1 $6$ $22$ $C_2^2\times C_6$ 3A1 2D 6D-1 $ac^{4}$
$D_{22}:C_{12}$ 6D-1 $6$ $22$ $C_2^2\times C_6$ 3A-1 2D 6D1 $ac^{8}$
$D_{22}:C_{12}$ 6E1 $6$ $22$ $C_2^2\times C_6$ 3A-1 2E 6E-1 $ac^{2}$
$D_{22}:C_{12}$ 6E-1 $6$ $22$ $C_2^2\times C_6$ 3A1 2E 6E1 $ac^{10}$
$D_{22}:C_{12}$ 11A1 $11$ $2$ $C_2\times C_{132}$ 11A2 11A3 11A5 $c^{24}$
$D_{22}:C_{12}$ 11A2 $11$ $2$ $C_2\times C_{132}$ 11A4 11A5 11A1 $c^{48}$
$D_{22}:C_{12}$ 11A3 $11$ $2$ $C_2\times C_{132}$ 11A5 11A2 11A4 $c^{72}$
$D_{22}:C_{12}$ 11A4 $11$ $2$ $C_2\times C_{132}$ 11A3 11A1 11A2 $c^{96}$
$D_{22}:C_{12}$ 11A5 $11$ $2$ $C_2\times C_{132}$ 11A1 11A4 11A3 $c^{120}$
$D_{22}:C_{12}$ 12A1 $12$ $2$ $C_2\times C_{132}$ 6C1 4A1 12A5 $c^{11}$
$D_{22}:C_{12}$ 12A-1 $12$ $2$ $C_2\times C_{132}$ 6C-1 4A-1 12A-5 $c^{121}$
$D_{22}:C_{12}$ 12A5 $12$ $2$ $C_2\times C_{132}$ 6C-1 4A1 12A1 $c^{55}$
$D_{22}:C_{12}$ 12A-5 $12$ $2$ $C_2\times C_{132}$ 6C1 4A-1 12A-1 $c^{77}$
$D_{22}:C_{12}$ 12B1 $12$ $22$ $C_2\times C_{12}$ 6A1 4B1 12B5 $ac$
$D_{22}:C_{12}$ 12B-1 $12$ $22$ $C_2\times C_{12}$ 6A-1 4B-1 12B-5 $ac^{11}$
$D_{22}:C_{12}$ 12B5 $12$ $22$ $C_2\times C_{12}$ 6A-1 4B1 12B1 $ac^{5}$
$D_{22}:C_{12}$ 12B-5 $12$ $22$ $C_2\times C_{12}$ 6A1 4B-1 12B-1 $ac^{7}$
$D_{22}:C_{12}$ 22A1 $22$ $2$ $C_2\times C_{132}$ 11A1 22A3 22A5 $bc^{12}$
$D_{22}:C_{12}$ 22A3 $22$ $2$ $C_2\times C_{132}$ 11A3 22A9 22A7 $bc^{36}$
$D_{22}:C_{12}$ 22A5 $22$ $2$ $C_2\times C_{132}$ 11A5 22A7 22A3 $bc^{60}$
$D_{22}:C_{12}$ 22A7 $22$ $2$ $C_2\times C_{132}$ 11A4 22A1 22A9 $bc^{84}$
$D_{22}:C_{12}$ 22A9 $22$ $2$ $C_2\times C_{132}$ 11A2 22A5 22A1 $bc^{108}$
$D_{22}:C_{12}$ 22B1 $22$ $2$ $C_2\times C_{132}$ 11A5 22B3 22B5 $bc^{6}$
$D_{22}:C_{12}$ 22B3 $22$ $2$ $C_2\times C_{132}$ 11A4 22B9 22B7 $bc^{18}$
$D_{22}:C_{12}$ 22B5 $22$ $2$ $C_2\times C_{132}$ 11A3 22B7 22B3 $bc^{30}$
$D_{22}:C_{12}$ 22B7 $22$ $2$ $C_2\times C_{132}$ 11A2 22B1 22B9 $bc^{42}$
$D_{22}:C_{12}$ 22B9 $22$ $2$ $C_2\times C_{132}$ 11A1 22B5 22B1 $bc^{54}$
$D_{22}:C_{12}$ 22C1 $22$ $2$ $C_2\times C_{132}$ 11A5 22C3 22C5 $c^{6}$
$D_{22}:C_{12}$ 22C3 $22$ $2$ $C_2\times C_{132}$ 11A4 22C9 22C7 $c^{18}$
$D_{22}:C_{12}$ 22C5 $22$ $2$ $C_2\times C_{132}$ 11A3 22C7 22C3 $c^{30}$
$D_{22}:C_{12}$ 22C7 $22$ $2$ $C_2\times C_{132}$ 11A2 22C1 22C9 $c^{42}$
$D_{22}:C_{12}$ 22C9 $22$ $2$ $C_2\times C_{132}$ 11A1 22C5 22C1 $c^{54}$
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