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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{2}=c^{198}=[a,b]=[a,c]=1, c^{b}=c^{109} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 11P
$C_{18}\times D_{22}$ 1A $1$ $1$ $C_{18}\times D_{22}$ 1A 1A 1A $1$
$C_{18}\times D_{22}$ 2A $2$ $1$ $C_{18}\times D_{22}$ 1A 2A 2A $c^{99}$
$C_{18}\times D_{22}$ 2B $2$ $1$ $C_{18}\times D_{22}$ 1A 2B 2B $a$
$C_{18}\times D_{22}$ 2C $2$ $1$ $C_{18}\times D_{22}$ 1A 2C 2C $ac^{99}$
$C_{18}\times D_{22}$ 2D $2$ $11$ $C_2^2\times C_{18}$ 1A 2D 2D $bc^{90}$
$C_{18}\times D_{22}$ 2E $2$ $11$ $C_2^2\times C_{18}$ 1A 2E 2E $bc^{45}$
$C_{18}\times D_{22}$ 2F $2$ $11$ $C_2^2\times C_{18}$ 1A 2F 2F $abc^{90}$
$C_{18}\times D_{22}$ 2G $2$ $11$ $C_2^2\times C_{18}$ 1A 2G 2G $abc^{45}$
$C_{18}\times D_{22}$ 3A1 $3$ $1$ $C_{18}\times D_{22}$ 3A-1 1A 3A-1 $c^{66}$
$C_{18}\times D_{22}$ 3A-1 $3$ $1$ $C_{18}\times D_{22}$ 3A1 1A 3A1 $c^{132}$
$C_{18}\times D_{22}$ 6A1 $6$ $1$ $C_{18}\times D_{22}$ 3A1 2A 6A-1 $c^{33}$
$C_{18}\times D_{22}$ 6A-1 $6$ $1$ $C_{18}\times D_{22}$ 3A-1 2A 6A1 $c^{165}$
$C_{18}\times D_{22}$ 6B1 $6$ $1$ $C_{18}\times D_{22}$ 3A-1 2B 6B-1 $ac^{66}$
$C_{18}\times D_{22}$ 6B-1 $6$ $1$ $C_{18}\times D_{22}$ 3A1 2B 6B1 $ac^{132}$
$C_{18}\times D_{22}$ 6C1 $6$ $1$ $C_{18}\times D_{22}$ 3A1 2C 6C-1 $ac^{33}$
$C_{18}\times D_{22}$ 6C-1 $6$ $1$ $C_{18}\times D_{22}$ 3A-1 2C 6C1 $ac^{165}$
$C_{18}\times D_{22}$ 6D1 $6$ $11$ $C_2^2\times C_{18}$ 3A1 2D 6D-1 $bc^{24}$
$C_{18}\times D_{22}$ 6D-1 $6$ $11$ $C_2^2\times C_{18}$ 3A-1 2D 6D1 $bc^{156}$
$C_{18}\times D_{22}$ 6E1 $6$ $11$ $C_2^2\times C_{18}$ 3A-1 2E 6E-1 $bc^{111}$
$C_{18}\times D_{22}$ 6E-1 $6$ $11$ $C_2^2\times C_{18}$ 3A1 2E 6E1 $bc^{177}$
$C_{18}\times D_{22}$ 6F1 $6$ $11$ $C_2^2\times C_{18}$ 3A1 2F 6F-1 $abc^{24}$
$C_{18}\times D_{22}$ 6F-1 $6$ $11$ $C_2^2\times C_{18}$ 3A-1 2F 6F1 $abc^{156}$
$C_{18}\times D_{22}$ 6G1 $6$ $11$ $C_2^2\times C_{18}$ 3A-1 2G 6G-1 $abc^{111}$
$C_{18}\times D_{22}$ 6G-1 $6$ $11$ $C_2^2\times C_{18}$ 3A1 2G 6G1 $abc^{177}$
$C_{18}\times D_{22}$ 9A1 $9$ $1$ $C_{18}\times D_{22}$ 9A2 3A1 9A-4 $c^{22}$
$C_{18}\times D_{22}$ 9A-1 $9$ $1$ $C_{18}\times D_{22}$ 9A-2 3A-1 9A4 $c^{176}$
$C_{18}\times D_{22}$ 9A2 $9$ $1$ $C_{18}\times D_{22}$ 9A4 3A-1 9A1 $c^{44}$
$C_{18}\times D_{22}$ 9A-2 $9$ $1$ $C_{18}\times D_{22}$ 9A-4 3A1 9A-1 $c^{154}$
$C_{18}\times D_{22}$ 9A4 $9$ $1$ $C_{18}\times D_{22}$ 9A-1 3A1 9A2 $c^{88}$
$C_{18}\times D_{22}$ 9A-4 $9$ $1$ $C_{18}\times D_{22}$ 9A1 3A-1 9A-2 $c^{110}$
$C_{18}\times D_{22}$ 11A1 $11$ $2$ $C_2\times C_{198}$ 11A2 11A3 11A5 $c^{18}$
$C_{18}\times D_{22}$ 11A2 $11$ $2$ $C_2\times C_{198}$ 11A4 11A5 11A1 $c^{36}$
$C_{18}\times D_{22}$ 11A3 $11$ $2$ $C_2\times C_{198}$ 11A5 11A2 11A4 $c^{54}$
$C_{18}\times D_{22}$ 11A4 $11$ $2$ $C_2\times C_{198}$ 11A3 11A1 11A2 $c^{72}$
$C_{18}\times D_{22}$ 11A5 $11$ $2$ $C_2\times C_{198}$ 11A1 11A4 11A3 $c^{90}$
$C_{18}\times D_{22}$ 18A1 $18$ $1$ $C_{18}\times D_{22}$ 9A1 6A1 18A5 $c^{11}$
$C_{18}\times D_{22}$ 18A-1 $18$ $1$ $C_{18}\times D_{22}$ 9A-1 6A-1 18A-5 $c^{187}$
$C_{18}\times D_{22}$ 18A5 $18$ $1$ $C_{18}\times D_{22}$ 9A-4 6A-1 18A7 $c^{55}$
$C_{18}\times D_{22}$ 18A-5 $18$ $1$ $C_{18}\times D_{22}$ 9A4 6A1 18A-7 $c^{143}$
$C_{18}\times D_{22}$ 18A7 $18$ $1$ $C_{18}\times D_{22}$ 9A-2 6A1 18A-1 $c^{77}$
$C_{18}\times D_{22}$ 18A-7 $18$ $1$ $C_{18}\times D_{22}$ 9A2 6A-1 18A1 $c^{121}$
$C_{18}\times D_{22}$ 18B1 $18$ $1$ $C_{18}\times D_{22}$ 9A2 6B1 18B5 $ac^{22}$
$C_{18}\times D_{22}$ 18B-1 $18$ $1$ $C_{18}\times D_{22}$ 9A-2 6B-1 18B-5 $ac^{176}$
$C_{18}\times D_{22}$ 18B5 $18$ $1$ $C_{18}\times D_{22}$ 9A1 6B-1 18B7 $ac^{110}$
$C_{18}\times D_{22}$ 18B-5 $18$ $1$ $C_{18}\times D_{22}$ 9A-1 6B1 18B-7 $ac^{88}$
$C_{18}\times D_{22}$ 18B7 $18$ $1$ $C_{18}\times D_{22}$ 9A-4 6B1 18B-1 $ac^{154}$
$C_{18}\times D_{22}$ 18B-7 $18$ $1$ $C_{18}\times D_{22}$ 9A4 6B-1 18B1 $ac^{44}$
$C_{18}\times D_{22}$ 18C1 $18$ $1$ $C_{18}\times D_{22}$ 9A1 6C1 18C5 $ac^{11}$
$C_{18}\times D_{22}$ 18C-1 $18$ $1$ $C_{18}\times D_{22}$ 9A-1 6C-1 18C-5 $ac^{187}$
$C_{18}\times D_{22}$ 18C5 $18$ $1$ $C_{18}\times D_{22}$ 9A-4 6C-1 18C7 $ac^{55}$
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