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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{2}=b^{8}=c^{14}=d^{6}=[a,d]=[b,d]=1, b^{a}=b^{7}, c^{a}=b^{4}c^{13}, c^{b}=cd^{3}, d^{c}=d^{5} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P
$(C_6\times D_{56}):C_2$ 1A $1$ $1$ $(C_6\times D_{56}):C_2$ 1A 1A 1A $1$
$(C_6\times D_{56}):C_2$ 2A $2$ $1$ $(C_6\times D_{56}):C_2$ 1A 2A 2A $b^{4}$
$(C_6\times D_{56}):C_2$ 2B $2$ $1$ $(C_6\times D_{56}):C_2$ 1A 2B 2B $d^{3}$
$(C_6\times D_{56}):C_2$ 2C $2$ $1$ $(C_6\times D_{56}):C_2$ 1A 2C 2C $b^{4}d^{3}$
$(C_6\times D_{56}):C_2$ 2D $2$ $12$ $C_2^2\times C_{28}$ 1A 2D 2D $c^{7}$
$(C_6\times D_{56}):C_2$ 2E $2$ $28$ $C_6.C_2^3$ 1A 2E 2E $ad^{3}$
$(C_6\times D_{56}):C_2$ 2F $2$ $28$ $C_6.C_2^3$ 1A 2F 2F $ab^{2}c^{10}$
$(C_6\times D_{56}):C_2$ 2G $2$ $56$ $C_2^2\times C_6$ 1A 2G 2G $abd^{3}$
$(C_6\times D_{56}):C_2$ 3A $3$ $2$ $C_6\times D_{56}$ 3A 1A 3A $d^{2}$
$(C_6\times D_{56}):C_2$ 4A $4$ $2$ $D_6:C_{56}$ 2A 4A 4A $b^{6}d^{3}$
$(C_6\times D_{56}):C_2$ 4B $4$ $2$ $D_6:C_{56}$ 2A 4B 4B $b^{2}$
$(C_6\times D_{56}):C_2$ 4C1 $4$ $6$ $D_{28}:C_2^2$ 2A 4C-1 4C-1 $b^{6}c^{7}$
$(C_6\times D_{56}):C_2$ 4C-1 $4$ $6$ $D_{28}:C_2^2$ 2A 4C1 4C1 $b^{2}c^{7}$
$(C_6\times D_{56}):C_2$ 4D $4$ $84$ $C_2^2\times C_4$ 2A 4D 4D $ab^{4}c^{13}$
$(C_6\times D_{56}):C_2$ 4E $4$ $84$ $C_2^2\times C_4$ 2A 4E 4E $ab^{4}c^{5}d^{5}$
$(C_6\times D_{56}):C_2$ 4F $4$ $168$ $C_2\times C_4$ 2C 4F 4F $ab^{5}cd^{5}$
$(C_6\times D_{56}):C_2$ 6A $6$ $2$ $C_6\times D_{56}$ 3A 2B 6A $d$
$(C_6\times D_{56}):C_2$ 6B $6$ $2$ $C_6\times D_{56}$ 3A 2C 6B $b^{4}d$
$(C_6\times D_{56}):C_2$ 6C $6$ $2$ $C_6\times D_{56}$ 3A 2A 6C $b^{4}d^{2}$
$(C_6\times D_{56}):C_2$ 6D $6$ $56$ $C_2^2\times C_6$ 3A 2E 6D $ad^{5}$
$(C_6\times D_{56}):C_2$ 6E $6$ $56$ $C_2^2\times C_6$ 3A 2F 6E $ab^{2}c^{10}d^{4}$
$(C_6\times D_{56}):C_2$ 6F1 $6$ $56$ $C_2^2\times C_6$ 3A 2G 6F1 $abd$
$(C_6\times D_{56}):C_2$ 6F-1 $6$ $56$ $C_2^2\times C_6$ 3A 2G 6F-1 $abd^{5}$
$(C_6\times D_{56}):C_2$ 7A1 $7$ $2$ $D_6:C_{56}$ 7A2 7A3 1A $c^{2}$
$(C_6\times D_{56}):C_2$ 7A2 $7$ $2$ $D_6:C_{56}$ 7A3 7A1 1A $c^{4}$
$(C_6\times D_{56}):C_2$ 7A3 $7$ $2$ $D_6:C_{56}$ 7A1 7A2 1A $c^{6}$
$(C_6\times D_{56}):C_2$ 8A1 $8$ $4$ $C_2\times C_{168}$ 4B 8A3 8A1 $b^{5}$
$(C_6\times D_{56}):C_2$ 8A3 $8$ $4$ $C_2\times C_{168}$ 4B 8A1 8A3 $b^{7}$
$(C_6\times D_{56}):C_2$ 8B1 $8$ $12$ $C_2\times C_{56}$ 4A 8B1 8B-1 $b^{7}c^{7}d^{3}$
$(C_6\times D_{56}):C_2$ 8B-1 $8$ $12$ $C_2\times C_{56}$ 4A 8B-1 8B1 $bc^{7}$
$(C_6\times D_{56}):C_2$ 12A $12$ $4$ $C_2\times C_{168}$ 6C 4A 12A $b^{6}d$
$(C_6\times D_{56}):C_2$ 12B $12$ $4$ $C_2\times C_{168}$ 6C 4B 12B $b^{6}d^{4}$
$(C_6\times D_{56}):C_2$ 14A1 $14$ $2$ $D_6:C_{56}$ 7A2 14A3 2A $b^{4}c^{2}$
$(C_6\times D_{56}):C_2$ 14A3 $14$ $2$ $D_6:C_{56}$ 7A1 14A5 2A $b^{4}c^{6}$
$(C_6\times D_{56}):C_2$ 14A5 $14$ $2$ $D_6:C_{56}$ 7A3 14A1 2A $b^{4}c^{10}$
$(C_6\times D_{56}):C_2$ 14B1 $14$ $2$ $D_6:C_{56}$ 7A1 14B3 2B $c^{6}d^{3}$
$(C_6\times D_{56}):C_2$ 14B3 $14$ $2$ $D_6:C_{56}$ 7A3 14B5 2B $c^{4}d^{3}$
$(C_6\times D_{56}):C_2$ 14B5 $14$ $2$ $D_6:C_{56}$ 7A2 14B1 2B $c^{2}d^{3}$
$(C_6\times D_{56}):C_2$ 14C1 $14$ $2$ $D_6:C_{56}$ 7A1 14C3 2C $b^{4}c^{6}d^{3}$
$(C_6\times D_{56}):C_2$ 14C3 $14$ $2$ $D_6:C_{56}$ 7A3 14C5 2C $b^{4}c^{4}d^{3}$
$(C_6\times D_{56}):C_2$ 14C5 $14$ $2$ $D_6:C_{56}$ 7A2 14C1 2C $b^{4}c^{2}d^{3}$
$(C_6\times D_{56}):C_2$ 14D1 $14$ $12$ $C_2^2\times C_{28}$ 7A1 14D3 2D $c$
$(C_6\times D_{56}):C_2$ 14D-1 $14$ $12$ $C_2^2\times C_{28}$ 7A1 14D-3 2D $b^{4}c$
$(C_6\times D_{56}):C_2$ 14D3 $14$ $12$ $C_2^2\times C_{28}$ 7A3 14D-5 2D $c^{3}$
$(C_6\times D_{56}):C_2$ 14D-3 $14$ $12$ $C_2^2\times C_{28}$ 7A3 14D5 2D $c^{11}$
$(C_6\times D_{56}):C_2$ 14D5 $14$ $12$ $C_2^2\times C_{28}$ 7A2 14D1 2D $c^{5}$
$(C_6\times D_{56}):C_2$ 14D-5 $14$ $12$ $C_2^2\times C_{28}$ 7A2 14D-1 2D $c^{9}$
$(C_6\times D_{56}):C_2$ 21A1 $21$ $4$ $C_2\times C_{168}$ 21A2 7A1 3A $c^{4}d^{2}$
$(C_6\times D_{56}):C_2$ 21A2 $21$ $4$ $C_2\times C_{168}$ 21A4 7A2 3A $c^{8}d^{4}$
$(C_6\times D_{56}):C_2$ 21A4 $21$ $4$ $C_2\times C_{168}$ 21A1 7A3 3A $c^{2}d^{2}$
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