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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{20}=c^{44}=[a,c]=1, b^{a}=b^{11}c^{33}, c^{b}=c^{17} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$(D_4\times C_{11}):C_{20}$ 1A $1$ $1$ $(D_4\times C_{11}):C_{20}$ 1A 1A 1A $1$
$(D_4\times C_{11}):C_{20}$ 2A $2$ $1$ $(D_4\times C_{11}):C_{20}$ 1A 2A 2A $c^{22}$
$(D_4\times C_{11}):C_{20}$ 2B $2$ $2$ $C_{44}:C_{20}$ 1A 2B 2B $b^{10}$
$(D_4\times C_{11}):C_{20}$ 2C $2$ $4$ $C_{22}:C_{20}$ 1A 2C 2C $a$
$(D_4\times C_{11}):C_{20}$ 4A1 $4$ $1$ $(D_4\times C_{11}):C_{20}$ 2A 4A1 4A-1 $c^{11}$
$(D_4\times C_{11}):C_{20}$ 4A-1 $4$ $1$ $(D_4\times C_{11}):C_{20}$ 2A 4A-1 4A1 $c^{33}$
$(D_4\times C_{11}):C_{20}$ 4B $4$ $2$ $C_{44}:C_{20}$ 2A 4B 4B $b^{10}c^{33}$
$(D_4\times C_{11}):C_{20}$ 4C $4$ $4$ $C_{22}:C_{20}$ 2A 4C 4C $ac^{11}$
$(D_4\times C_{11}):C_{20}$ 4D1 $4$ $22$ $C_4\times C_{20}$ 2B 4D1 4D-1 $b^{5}$
$(D_4\times C_{11}):C_{20}$ 4D-1 $4$ $22$ $C_4\times C_{20}$ 2B 4D-1 4D1 $b^{15}$
$(D_4\times C_{11}):C_{20}$ 4E1 $4$ $22$ $C_4\times C_{20}$ 2B 4E1 4E-1 $b^{5}c^{30}$
$(D_4\times C_{11}):C_{20}$ 4E-1 $4$ $22$ $C_4\times C_{20}$ 2B 4E-1 4E1 $b^{15}c^{30}$
$(D_4\times C_{11}):C_{20}$ 5A1 $5$ $11$ $D_4:C_{20}$ 5A2 1A 5A1 $b^{8}c^{40}$
$(D_4\times C_{11}):C_{20}$ 5A-1 $5$ $11$ $D_4:C_{20}$ 5A-2 1A 5A-1 $b^{12}c^{12}$
$(D_4\times C_{11}):C_{20}$ 5A2 $5$ $11$ $D_4:C_{20}$ 5A-1 1A 5A2 $b^{16}c^{24}$
$(D_4\times C_{11}):C_{20}$ 5A-2 $5$ $11$ $D_4:C_{20}$ 5A1 1A 5A-2 $b^{4}c^{4}$
$(D_4\times C_{11}):C_{20}$ 8A1 $8$ $44$ $C_{40}$ 4A1 8A1 8A-1 $ab^{5}c^{33}$
$(D_4\times C_{11}):C_{20}$ 8A-1 $8$ $44$ $C_{40}$ 4A-1 8A-1 8A1 $ab^{5}c^{22}$
$(D_4\times C_{11}):C_{20}$ 10A1 $10$ $11$ $D_4:C_{20}$ 5A1 2A 10A1 $b^{4}c^{26}$
$(D_4\times C_{11}):C_{20}$ 10A-1 $10$ $11$ $D_4:C_{20}$ 5A-1 2A 10A-1 $b^{16}c^{2}$
$(D_4\times C_{11}):C_{20}$ 10A3 $10$ $11$ $D_4:C_{20}$ 5A-2 2A 10A3 $b^{12}c^{34}$
$(D_4\times C_{11}):C_{20}$ 10A-3 $10$ $11$ $D_4:C_{20}$ 5A2 2A 10A-3 $b^{8}c^{18}$
$(D_4\times C_{11}):C_{20}$ 10B1 $10$ $22$ $C_4\times C_{20}$ 5A-2 2B 10B1 $b^{2}$
$(D_4\times C_{11}):C_{20}$ 10B-1 $10$ $22$ $C_4\times C_{20}$ 5A2 2B 10B-1 $b^{18}$
$(D_4\times C_{11}):C_{20}$ 10B3 $10$ $22$ $C_4\times C_{20}$ 5A-1 2B 10B3 $b^{6}$
$(D_4\times C_{11}):C_{20}$ 10B-3 $10$ $22$ $C_4\times C_{20}$ 5A1 2B 10B-3 $b^{14}$
$(D_4\times C_{11}):C_{20}$ 10C1 $10$ $44$ $C_2\times C_{20}$ 5A2 2C 10C1 $ab^{8}c^{34}$
$(D_4\times C_{11}):C_{20}$ 10C-1 $10$ $44$ $C_2\times C_{20}$ 5A-2 2C 10C-1 $ab^{12}c^{30}$
$(D_4\times C_{11}):C_{20}$ 10C3 $10$ $44$ $C_2\times C_{20}$ 5A1 2C 10C3 $ab^{4}c^{10}$
$(D_4\times C_{11}):C_{20}$ 10C-3 $10$ $44$ $C_2\times C_{20}$ 5A-1 2C 10C-3 $ab^{16}c^{38}$
$(D_4\times C_{11}):C_{20}$ 11A $11$ $10$ $D_4:C_{22}$ 11A 11A 1A $c^{8}$
$(D_4\times C_{11}):C_{20}$ 20A1 $20$ $11$ $D_4:C_{20}$ 10A3 4A1 20A-9 $b^{16}c^{11}$
$(D_4\times C_{11}):C_{20}$ 20A-1 $20$ $11$ $D_4:C_{20}$ 10A-3 4A-1 20A9 $b^{4}c^{33}$
$(D_4\times C_{11}):C_{20}$ 20A3 $20$ $11$ $D_4:C_{20}$ 10A-1 4A-1 20A-7 $b^{8}c^{33}$
$(D_4\times C_{11}):C_{20}$ 20A-3 $20$ $11$ $D_4:C_{20}$ 10A1 4A1 20A7 $b^{12}c^{11}$
$(D_4\times C_{11}):C_{20}$ 20A7 $20$ $11$ $D_4:C_{20}$ 10A1 4A-1 20A-3 $b^{12}c^{33}$
$(D_4\times C_{11}):C_{20}$ 20A-7 $20$ $11$ $D_4:C_{20}$ 10A-1 4A1 20A3 $b^{8}c^{11}$
$(D_4\times C_{11}):C_{20}$ 20A9 $20$ $11$ $D_4:C_{20}$ 10A-3 4A1 20A-1 $b^{4}c^{11}$
$(D_4\times C_{11}):C_{20}$ 20A-9 $20$ $11$ $D_4:C_{20}$ 10A3 4A-1 20A1 $b^{16}c^{33}$
$(D_4\times C_{11}):C_{20}$ 20B1 $20$ $22$ $C_4\times C_{20}$ 10A1 4B 20B1 $b^{2}c$
$(D_4\times C_{11}):C_{20}$ 20B-1 $20$ $22$ $C_4\times C_{20}$ 10A-1 4B 20B-1 $b^{18}c$
$(D_4\times C_{11}):C_{20}$ 20B3 $20$ $22$ $C_4\times C_{20}$ 10A3 4B 20B3 $b^{6}c$
$(D_4\times C_{11}):C_{20}$ 20B-3 $20$ $22$ $C_4\times C_{20}$ 10A-3 4B 20B-3 $b^{14}c$
$(D_4\times C_{11}):C_{20}$ 20C1 $20$ $22$ $C_4\times C_{20}$ 10B1 4D1 20C-9 $b$
$(D_4\times C_{11}):C_{20}$ 20C-1 $20$ $22$ $C_4\times C_{20}$ 10B-1 4D-1 20C9 $b^{19}$
$(D_4\times C_{11}):C_{20}$ 20C3 $20$ $22$ $C_4\times C_{20}$ 10B3 4D-1 20C-7 $b^{3}$
$(D_4\times C_{11}):C_{20}$ 20C-3 $20$ $22$ $C_4\times C_{20}$ 10B-3 4D1 20C7 $b^{17}$
$(D_4\times C_{11}):C_{20}$ 20C7 $20$ $22$ $C_4\times C_{20}$ 10B-3 4D-1 20C-3 $b^{7}$
$(D_4\times C_{11}):C_{20}$ 20C-7 $20$ $22$ $C_4\times C_{20}$ 10B3 4D1 20C3 $b^{13}$
$(D_4\times C_{11}):C_{20}$ 20C9 $20$ $22$ $C_4\times C_{20}$ 10B-1 4D1 20C-1 $b^{9}$
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