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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{8}=c^{16}=[b,c]=1, b^{a}=bc^{14}, c^{a}=b^{5}c^{15} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$(C_8\times C_{16}):C_4$ 1A $1$ $1$ $(C_8\times C_{16}):C_4$ 1A $1$
$(C_8\times C_{16}):C_4$ 2A $2$ $1$ $(C_8\times C_{16}):C_4$ 1A $c^{8}$
$(C_8\times C_{16}):C_4$ 2B $2$ $2$ $C_{16}:D_8$ 1A $b^{4}$
$(C_8\times C_{16}):C_4$ 2C $2$ $32$ $C_2^2:C_4$ 1A $a^{2}b^{7}c^{2}$
$(C_8\times C_{16}):C_4$ 2D $2$ $32$ $C_2^2:C_4$ 1A $a^{2}b^{4}c^{10}$
$(C_8\times C_{16}):C_4$ 4A $4$ $4$ $C_8\times C_{16}$ 2B $b^{2}$
$(C_8\times C_{16}):C_4$ 4B $4$ $4$ $C_8\times C_{16}$ 2B $b^{2}c^{8}$
$(C_8\times C_{16}):C_4$ 4C $4$ $4$ $C_8\times C_{16}$ 2A $c^{4}$
$(C_8\times C_{16}):C_4$ 4D $4$ $64$ $C_2\times C_4$ 2A $a^{2}b^{7}c^{7}$
$(C_8\times C_{16}):C_4$ 4E1 $4$ $64$ $C_2\times C_4$ 2C $a^{3}c^{5}$
$(C_8\times C_{16}):C_4$ 4E-1 $4$ $64$ $C_2\times C_4$ 2C $ab^{7}c^{5}$
$(C_8\times C_{16}):C_4$ 4F1 $4$ $64$ $C_2\times C_4$ 2D $ab^{3}c^{6}$
$(C_8\times C_{16}):C_4$ 4F-1 $4$ $64$ $C_2\times C_4$ 2D $a^{3}bc^{4}$
$(C_8\times C_{16}):C_4$ 8A1 $8$ $4$ $C_8\times C_{16}$ 4A $b$
$(C_8\times C_{16}):C_4$ 8A3 $8$ $4$ $C_8\times C_{16}$ 4A $b^{5}$
$(C_8\times C_{16}):C_4$ 8B1 $8$ $4$ $C_8\times C_{16}$ 4A $bc^{8}$
$(C_8\times C_{16}):C_4$ 8B3 $8$ $4$ $C_8\times C_{16}$ 4A $b^{5}c^{8}$
$(C_8\times C_{16}):C_4$ 8C1 $8$ $4$ $C_8\times C_{16}$ 4B $bc^{4}$
$(C_8\times C_{16}):C_4$ 8C3 $8$ $4$ $C_8\times C_{16}$ 4B $bc^{2}$
$(C_8\times C_{16}):C_4$ 8D1 $8$ $4$ $C_8\times C_{16}$ 4B $bc^{12}$
$(C_8\times C_{16}):C_4$ 8D3 $8$ $4$ $C_8\times C_{16}$ 4B $bc^{10}$
$(C_8\times C_{16}):C_4$ 8E1 $8$ $4$ $C_8\times C_{16}$ 4C $c^{2}$
$(C_8\times C_{16}):C_4$ 8E3 $8$ $4$ $C_8\times C_{16}$ 4C $c^{6}$
$(C_8\times C_{16}):C_4$ 8F1 $8$ $4$ $C_8\times C_{16}$ 4C $b^{4}c^{2}$
$(C_8\times C_{16}):C_4$ 8F3 $8$ $4$ $C_8\times C_{16}$ 4C $b^{4}c^{6}$
$(C_8\times C_{16}):C_4$ 16A1 $16$ $4$ $C_8\times C_{16}$ 8E1 $c$
$(C_8\times C_{16}):C_4$ 16A-1 $16$ $4$ $C_8\times C_{16}$ 8E1 $c^{9}$
$(C_8\times C_{16}):C_4$ 16A3 $16$ $4$ $C_8\times C_{16}$ 8E3 $c^{5}$
$(C_8\times C_{16}):C_4$ 16A-3 $16$ $4$ $C_8\times C_{16}$ 8E3 $c^{13}$
$(C_8\times C_{16}):C_4$ 16B1 $16$ $4$ $C_8\times C_{16}$ 8E1 $b^{4}c$
$(C_8\times C_{16}):C_4$ 16B-1 $16$ $4$ $C_8\times C_{16}$ 8E1 $b^{4}c^{9}$
$(C_8\times C_{16}):C_4$ 16B3 $16$ $4$ $C_8\times C_{16}$ 8E3 $b^{4}c^{5}$
$(C_8\times C_{16}):C_4$ 16B-3 $16$ $4$ $C_8\times C_{16}$ 8E3 $b^{4}c^{13}$
$(C_8\times C_{16}):C_4$ 16C1 $16$ $4$ $C_8\times C_{16}$ 8F1 $b^{2}c$
$(C_8\times C_{16}):C_4$ 16C-1 $16$ $4$ $C_8\times C_{16}$ 8F1 $b^{2}c^{9}$
$(C_8\times C_{16}):C_4$ 16C3 $16$ $4$ $C_8\times C_{16}$ 8F3 $b^{2}c^{5}$
$(C_8\times C_{16}):C_4$ 16C-3 $16$ $4$ $C_8\times C_{16}$ 8F3 $b^{2}c^{13}$
$(C_8\times C_{16}):C_4$ 16D1 $16$ $4$ $C_8\times C_{16}$ 8F3 $bc$
$(C_8\times C_{16}):C_4$ 16D-1 $16$ $4$ $C_8\times C_{16}$ 8F3 $b^{2}c^{3}$
$(C_8\times C_{16}):C_4$ 16D3 $16$ $4$ $C_8\times C_{16}$ 8F1 $b^{6}c$
$(C_8\times C_{16}):C_4$ 16D-3 $16$ $4$ $C_8\times C_{16}$ 8F1 $b^{6}c^{9}$
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