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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{2}=c^{396}=[a,b]=[b,c]=1, c^{a}=bc^{109} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 11P
$D_{22}:C_{36}$ 1A $1$ $1$ $D_{22}:C_{36}$ 1A 1A 1A $1$
$D_{22}:C_{36}$ 2A $2$ $1$ $D_{22}:C_{36}$ 1A 2A 2A $bc^{198}$
$D_{22}:C_{36}$ 2B $2$ $1$ $D_{22}:C_{36}$ 1A 2B 2B $b$
$D_{22}:C_{36}$ 2C $2$ $1$ $D_{22}:C_{36}$ 1A 2C 2C $c^{198}$
$D_{22}:C_{36}$ 2D $2$ $22$ $C_2^2\times C_{18}$ 1A 2D 2D $ac^{180}$
$D_{22}:C_{36}$ 2E $2$ $22$ $C_2^2\times C_{18}$ 1A 2E 2E $ac^{90}$
$D_{22}:C_{36}$ 3A1 $3$ $1$ $D_{22}:C_{36}$ 3A-1 1A 3A-1 $c^{132}$
$D_{22}:C_{36}$ 3A-1 $3$ $1$ $D_{22}:C_{36}$ 3A1 1A 3A1 $c^{264}$
$D_{22}:C_{36}$ 4A1 $4$ $2$ $C_2\times C_{396}$ 2C 4A-1 4A1 $c^{99}$
$D_{22}:C_{36}$ 4A-1 $4$ $2$ $C_2\times C_{396}$ 2C 4A1 4A-1 $c^{297}$
$D_{22}:C_{36}$ 4B1 $4$ $22$ $C_2\times C_{36}$ 2A 4B-1 4B1 $ac^{45}$
$D_{22}:C_{36}$ 4B-1 $4$ $22$ $C_2\times C_{36}$ 2A 4B1 4B-1 $abc^{243}$
$D_{22}:C_{36}$ 6A1 $6$ $1$ $D_{22}:C_{36}$ 3A-1 2A 6A-1 $bc^{330}$
$D_{22}:C_{36}$ 6A-1 $6$ $1$ $D_{22}:C_{36}$ 3A1 2A 6A1 $bc^{66}$
$D_{22}:C_{36}$ 6B1 $6$ $1$ $D_{22}:C_{36}$ 3A-1 2B 6B-1 $bc^{132}$
$D_{22}:C_{36}$ 6B-1 $6$ $1$ $D_{22}:C_{36}$ 3A1 2B 6B1 $bc^{264}$
$D_{22}:C_{36}$ 6C1 $6$ $1$ $D_{22}:C_{36}$ 3A1 2C 6C-1 $c^{66}$
$D_{22}:C_{36}$ 6C-1 $6$ $1$ $D_{22}:C_{36}$ 3A-1 2C 6C1 $c^{330}$
$D_{22}:C_{36}$ 6D1 $6$ $22$ $C_2^2\times C_{18}$ 3A1 2D 6D-1 $ac^{48}$
$D_{22}:C_{36}$ 6D-1 $6$ $22$ $C_2^2\times C_{18}$ 3A-1 2D 6D1 $ac^{312}$
$D_{22}:C_{36}$ 6E1 $6$ $22$ $C_2^2\times C_{18}$ 3A-1 2E 6E-1 $ac^{222}$
$D_{22}:C_{36}$ 6E-1 $6$ $22$ $C_2^2\times C_{18}$ 3A1 2E 6E1 $ac^{354}$
$D_{22}:C_{36}$ 9A1 $9$ $1$ $D_{22}:C_{36}$ 9A2 3A1 9A-4 $c^{44}$
$D_{22}:C_{36}$ 9A-1 $9$ $1$ $D_{22}:C_{36}$ 9A-2 3A-1 9A4 $c^{352}$
$D_{22}:C_{36}$ 9A2 $9$ $1$ $D_{22}:C_{36}$ 9A4 3A-1 9A1 $c^{88}$
$D_{22}:C_{36}$ 9A-2 $9$ $1$ $D_{22}:C_{36}$ 9A-4 3A1 9A-1 $c^{308}$
$D_{22}:C_{36}$ 9A4 $9$ $1$ $D_{22}:C_{36}$ 9A-1 3A1 9A2 $c^{176}$
$D_{22}:C_{36}$ 9A-4 $9$ $1$ $D_{22}:C_{36}$ 9A1 3A-1 9A-2 $c^{220}$
$D_{22}:C_{36}$ 11A1 $11$ $2$ $C_2\times C_{396}$ 11A2 11A3 11A5 $c^{72}$
$D_{22}:C_{36}$ 11A2 $11$ $2$ $C_2\times C_{396}$ 11A4 11A5 11A1 $c^{144}$
$D_{22}:C_{36}$ 11A3 $11$ $2$ $C_2\times C_{396}$ 11A5 11A2 11A4 $c^{216}$
$D_{22}:C_{36}$ 11A4 $11$ $2$ $C_2\times C_{396}$ 11A3 11A1 11A2 $c^{288}$
$D_{22}:C_{36}$ 11A5 $11$ $2$ $C_2\times C_{396}$ 11A1 11A4 11A3 $c^{360}$
$D_{22}:C_{36}$ 12A1 $12$ $2$ $C_2\times C_{396}$ 6C1 4A1 12A5 $c^{33}$
$D_{22}:C_{36}$ 12A-1 $12$ $2$ $C_2\times C_{396}$ 6C-1 4A-1 12A-5 $c^{363}$
$D_{22}:C_{36}$ 12A5 $12$ $2$ $C_2\times C_{396}$ 6C-1 4A1 12A1 $c^{165}$
$D_{22}:C_{36}$ 12A-5 $12$ $2$ $C_2\times C_{396}$ 6C1 4A-1 12A-1 $c^{231}$
$D_{22}:C_{36}$ 12B1 $12$ $22$ $C_2\times C_{36}$ 6A1 4B1 12B5 $abc^{111}$
$D_{22}:C_{36}$ 12B-1 $12$ $22$ $C_2\times C_{36}$ 6A-1 4B-1 12B-5 $ac^{177}$
$D_{22}:C_{36}$ 12B5 $12$ $22$ $C_2\times C_{36}$ 6A-1 4B1 12B1 $abc^{375}$
$D_{22}:C_{36}$ 12B-5 $12$ $22$ $C_2\times C_{36}$ 6A1 4B-1 12B-1 $ac^{309}$
$D_{22}:C_{36}$ 18A1 $18$ $1$ $D_{22}:C_{36}$ 9A-4 6A1 18A5 $bc^{110}$
$D_{22}:C_{36}$ 18A-1 $18$ $1$ $D_{22}:C_{36}$ 9A4 6A-1 18A-5 $bc^{286}$
$D_{22}:C_{36}$ 18A5 $18$ $1$ $D_{22}:C_{36}$ 9A-2 6A-1 18A7 $bc^{154}$
$D_{22}:C_{36}$ 18A-5 $18$ $1$ $D_{22}:C_{36}$ 9A2 6A1 18A-7 $bc^{242}$
$D_{22}:C_{36}$ 18A7 $18$ $1$ $D_{22}:C_{36}$ 9A-1 6A1 18A-1 $bc^{374}$
$D_{22}:C_{36}$ 18A-7 $18$ $1$ $D_{22}:C_{36}$ 9A1 6A-1 18A1 $bc^{22}$
$D_{22}:C_{36}$ 18B1 $18$ $1$ $D_{22}:C_{36}$ 9A2 6B1 18B5 $bc^{44}$
$D_{22}:C_{36}$ 18B-1 $18$ $1$ $D_{22}:C_{36}$ 9A-2 6B-1 18B-5 $bc^{352}$
$D_{22}:C_{36}$ 18B5 $18$ $1$ $D_{22}:C_{36}$ 9A1 6B-1 18B7 $bc^{220}$
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