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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid b^{10}=c^{11}=d^{11}=[c,d]=1, a^{4}=c^{2}d^{10}, b^{a}=b^{9}c^{6}d^{2}, c^{a}=cd^{10}, d^{a}=d^{10}, c^{b}=c^{8}d^{4}, d^{b}=c^{8} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 11P
$(C_{11}\times C_{22}).D_{10}$ 1A $1$ $1$ $(C_{11}\times C_{22}).D_{10}$ 1A 1A 1A $1$
$(C_{11}\times C_{22}).D_{10}$ 2A $2$ $1$ $(C_{11}\times C_{22}).D_{10}$ 1A 2A 2A $a^{2}c^{10}d^{6}$
$(C_{11}\times C_{22}).D_{10}$ 2B $2$ $121$ $C_{10}:C_4$ 1A 2B 2B $b^{5}c^{4}$
$(C_{11}\times C_{22}).D_{10}$ 2C $2$ $121$ $C_{10}:C_4$ 1A 2C 2C $a^{2}b^{5}c^{3}d^{3}$
$(C_{11}\times C_{22}).D_{10}$ 4A1 $4$ $55$ $C_4\times D_{11}$ 2A 4A1 4A-1 $ab^{4}c^{8}d^{2}$
$(C_{11}\times C_{22}).D_{10}$ 4A-1 $4$ $55$ $C_4\times D_{11}$ 2A 4A-1 4A1 $a^{3}b^{4}cd^{5}$
$(C_{11}\times C_{22}).D_{10}$ 4B1 $4$ $55$ $C_4\times D_{11}$ 2A 4B1 4B-1 $a^{3}bc^{5}d^{8}$
$(C_{11}\times C_{22}).D_{10}$ 4B-1 $4$ $55$ $C_4\times D_{11}$ 2A 4B-1 4B1 $abc^{9}d$
$(C_{11}\times C_{22}).D_{10}$ 5A1 $5$ $242$ $C_2\times C_{10}$ 5A2 1A 5A1 $b^{2}c^{7}d^{7}$
$(C_{11}\times C_{22}).D_{10}$ 5A2 $5$ $242$ $C_2\times C_{10}$ 5A1 1A 5A2 $b^{4}c^{5}d^{4}$
$(C_{11}\times C_{22}).D_{10}$ 10A1 $10$ $242$ $C_2\times C_{10}$ 5A1 2A 10A1 $a^{2}b^{6}c^{10}d^{2}$
$(C_{11}\times C_{22}).D_{10}$ 10A3 $10$ $242$ $C_2\times C_{10}$ 5A2 2A 10A3 $a^{2}b^{8}c^{6}d^{6}$
$(C_{11}\times C_{22}).D_{10}$ 10B1 $10$ $242$ $C_2\times C_{10}$ 5A1 2B 10B1 $b^{9}c^{2}d^{8}$
$(C_{11}\times C_{22}).D_{10}$ 10B3 $10$ $242$ $C_2\times C_{10}$ 5A2 2B 10B3 $b^{7}c^{7}d^{9}$
$(C_{11}\times C_{22}).D_{10}$ 10C1 $10$ $242$ $C_2\times C_{10}$ 5A1 2C 10C1 $a^{2}bc^{8}d^{2}$
$(C_{11}\times C_{22}).D_{10}$ 10C3 $10$ $242$ $C_2\times C_{10}$ 5A2 2C 10C3 $a^{2}b^{3}c^{7}$
$(C_{11}\times C_{22}).D_{10}$ 11A1 $11$ $10$ $C_{11}:C_{44}$ 11A2 11A5 1A $c^{4}d$
$(C_{11}\times C_{22}).D_{10}$ 11A2 $11$ $10$ $C_{11}:C_{44}$ 11A4 11A1 1A $c^{8}d^{2}$
$(C_{11}\times C_{22}).D_{10}$ 11A3 $11$ $10$ $C_{11}:C_{44}$ 11A5 11A4 1A $cd^{3}$
$(C_{11}\times C_{22}).D_{10}$ 11A4 $11$ $10$ $C_{11}:C_{44}$ 11A3 11A2 1A $c^{5}d^{4}$
$(C_{11}\times C_{22}).D_{10}$ 11A5 $11$ $10$ $C_{11}:C_{44}$ 11A1 11A3 1A $c^{9}d^{5}$
$(C_{11}\times C_{22}).D_{10}$ 11B1 $11$ $10$ $C_{11}:C_{44}$ 11B2 11B5 1A $c^{4}d^{5}$
$(C_{11}\times C_{22}).D_{10}$ 11B2 $11$ $10$ $C_{11}:C_{44}$ 11B4 11B1 1A $c^{8}d^{10}$
$(C_{11}\times C_{22}).D_{10}$ 11B3 $11$ $10$ $C_{11}:C_{44}$ 11B5 11B4 1A $cd^{4}$
$(C_{11}\times C_{22}).D_{10}$ 11B4 $11$ $10$ $C_{11}:C_{44}$ 11B3 11B2 1A $c^{5}d^{9}$
$(C_{11}\times C_{22}).D_{10}$ 11B5 $11$ $10$ $C_{11}:C_{44}$ 11B1 11B3 1A $c^{9}d^{3}$
$(C_{11}\times C_{22}).D_{10}$ 11C $11$ $20$ $C_{11}\times C_{22}$ 11C 11C 1A $c^{4}d^{10}$
$(C_{11}\times C_{22}).D_{10}$ 22A1 $22$ $10$ $C_{11}:C_{44}$ 11A1 22A5 2A $a^{2}cd$
$(C_{11}\times C_{22}).D_{10}$ 22A3 $22$ $10$ $C_{11}:C_{44}$ 11A3 22A7 2A $a^{2}c^{5}d^{2}$
$(C_{11}\times C_{22}).D_{10}$ 22A5 $22$ $10$ $C_{11}:C_{44}$ 11A5 22A3 2A $a^{2}c^{9}d^{3}$
$(C_{11}\times C_{22}).D_{10}$ 22A7 $22$ $10$ $C_{11}:C_{44}$ 11A4 22A9 2A $a^{2}c^{2}d^{4}$
$(C_{11}\times C_{22}).D_{10}$ 22A9 $22$ $10$ $C_{11}:C_{44}$ 11A2 22A1 2A $a^{2}c^{6}d^{5}$
$(C_{11}\times C_{22}).D_{10}$ 22B1 $22$ $10$ $C_{11}:C_{44}$ 11B1 22B5 2A $a^{2}cd^{3}$
$(C_{11}\times C_{22}).D_{10}$ 22B3 $22$ $10$ $C_{11}:C_{44}$ 11B3 22B7 2A $a^{2}c^{5}d^{8}$
$(C_{11}\times C_{22}).D_{10}$ 22B5 $22$ $10$ $C_{11}:C_{44}$ 11B5 22B3 2A $a^{2}c^{9}d^{2}$
$(C_{11}\times C_{22}).D_{10}$ 22B7 $22$ $10$ $C_{11}:C_{44}$ 11B4 22B9 2A $a^{2}c^{2}d^{7}$
$(C_{11}\times C_{22}).D_{10}$ 22B9 $22$ $10$ $C_{11}:C_{44}$ 11B2 22B1 2A $a^{2}c^{6}d$
$(C_{11}\times C_{22}).D_{10}$ 22C $22$ $20$ $C_{11}\times C_{22}$ 11C 22C 2A $a^{2}c$
$(C_{11}\times C_{22}).D_{10}$ 44A1 $44$ $110$ $C_{44}$ 22A1 44A5 4A1 $a^{3}b^{4}c^{2}d^{8}$
$(C_{11}\times C_{22}).D_{10}$ 44A-1 $44$ $110$ $C_{44}$ 22A1 44A-5 4A-1 $ab^{4}c^{7}d^{10}$
$(C_{11}\times C_{22}).D_{10}$ 44A3 $44$ $110$ $C_{44}$ 22A3 44A7 4A-1 $ab^{4}$
$(C_{11}\times C_{22}).D_{10}$ 44A-3 $44$ $110$ $C_{44}$ 22A3 44A-7 4A1 $a^{3}b^{4}c^{9}d^{7}$
$(C_{11}\times C_{22}).D_{10}$ 44A5 $44$ $110$ $C_{44}$ 22A5 44A-3 4A1 $a^{3}b^{4}c^{6}d^{9}$
$(C_{11}\times C_{22}).D_{10}$ 44A-5 $44$ $110$ $C_{44}$ 22A5 44A3 4A-1 $ab^{4}c^{3}d^{9}$
$(C_{11}\times C_{22}).D_{10}$ 44A7 $44$ $110$ $C_{44}$ 22A7 44A-9 4A-1 $ab^{4}c^{4}d$
$(C_{11}\times C_{22}).D_{10}$ 44A-7 $44$ $110$ $C_{44}$ 22A7 44A9 4A1 $a^{3}b^{4}c^{5}d^{6}$
$(C_{11}\times C_{22}).D_{10}$ 44A9 $44$ $110$ $C_{44}$ 22A9 44A1 4A1 $a^{3}b^{4}c^{10}d^{10}$
$(C_{11}\times C_{22}).D_{10}$ 44A-9 $44$ $110$ $C_{44}$ 22A9 44A-1 4A-1 $ab^{4}c^{10}d^{8}$
$(C_{11}\times C_{22}).D_{10}$ 44B1 $44$ $110$ $C_{44}$ 22B1 44B5 4B1 $abc^{10}d^{5}$
$(C_{11}\times C_{22}).D_{10}$ 44B-1 $44$ $110$ $C_{44}$ 22B1 44B-5 4B-1 $a^{3}bc^{4}d^{4}$
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