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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{6}=c^{77}=[a,b]=1, c^{a}=c^{34}, c^{b}=c^{32} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P 11P
$D_{11}\times F_7$ 1A $1$ $1$ $D_{11}\times F_7$ 1A 1A 1A 1A $1$
$D_{11}\times F_7$ 2A $2$ $7$ $C_3\times D_{22}$ 1A 2A 2A 2A $a$
$D_{11}\times F_7$ 2B $2$ $11$ $C_2\times F_7$ 1A 2B 2B 2B $b^{3}c^{7}$
$D_{11}\times F_7$ 2C $2$ $77$ $C_2\times C_6$ 1A 2C 2C 2C $ab^{3}c^{28}$
$D_{11}\times F_7$ 3A1 $3$ $7$ $C_3\times D_{22}$ 3A-1 1A 3A-1 3A1 $b^{2}$
$D_{11}\times F_7$ 3A-1 $3$ $7$ $C_3\times D_{22}$ 3A1 1A 3A1 3A-1 $b^{4}$
$D_{11}\times F_7$ 6A1 $6$ $7$ $C_3\times D_{22}$ 3A1 2A 6A-1 6A1 $ab^{4}$
$D_{11}\times F_7$ 6A-1 $6$ $7$ $C_3\times D_{22}$ 3A-1 2A 6A1 6A-1 $ab^{2}$
$D_{11}\times F_7$ 6B1 $6$ $77$ $C_2\times C_6$ 3A-1 2B 6B-1 6B1 $b^{5}c^{7}$
$D_{11}\times F_7$ 6B-1 $6$ $77$ $C_2\times C_6$ 3A1 2B 6B1 6B-1 $bc^{7}$
$D_{11}\times F_7$ 6C1 $6$ $77$ $C_2\times C_6$ 3A-1 2C 6C-1 6C1 $ab^{5}c^{28}$
$D_{11}\times F_7$ 6C-1 $6$ $77$ $C_2\times C_6$ 3A1 2C 6C1 6C-1 $abc^{28}$
$D_{11}\times F_7$ 7A $7$ $6$ $C_7\times D_{11}$ 7A 7A 7A 1A $c^{11}$
$D_{11}\times F_7$ 11A1 $11$ $2$ $C_{11}\times F_7$ 11A2 11A3 11A5 11A4 $c^{42}$
$D_{11}\times F_7$ 11A2 $11$ $2$ $C_{11}\times F_7$ 11A4 11A5 11A1 11A3 $c^{7}$
$D_{11}\times F_7$ 11A3 $11$ $2$ $C_{11}\times F_7$ 11A5 11A2 11A4 11A1 $c^{49}$
$D_{11}\times F_7$ 11A4 $11$ $2$ $C_{11}\times F_7$ 11A3 11A1 11A2 11A5 $c^{14}$
$D_{11}\times F_7$ 11A5 $11$ $2$ $C_{11}\times F_7$ 11A1 11A4 11A3 11A2 $c^{56}$
$D_{11}\times F_7$ 14A $14$ $66$ $C_{14}$ 7A 14A 14A 2B $b^{3}c^{60}$
$D_{11}\times F_7$ 22A1 $22$ $14$ $C_{66}$ 11A1 22A3 22A5 22A7 $ac^{21}$
$D_{11}\times F_7$ 22A3 $22$ $14$ $C_{66}$ 11A3 22A9 22A7 22A1 $ac^{63}$
$D_{11}\times F_7$ 22A5 $22$ $14$ $C_{66}$ 11A5 22A7 22A3 22A9 $ac^{28}$
$D_{11}\times F_7$ 22A7 $22$ $14$ $C_{66}$ 11A4 22A1 22A9 22A5 $ac^{70}$
$D_{11}\times F_7$ 22A9 $22$ $14$ $C_{66}$ 11A2 22A5 22A1 22A3 $ac^{35}$
$D_{11}\times F_7$ 33A1 $33$ $14$ $C_{66}$ 33A2 11A1 33A5 33A4 $b^{4}c^{14}$
$D_{11}\times F_7$ 33A-1 $33$ $14$ $C_{66}$ 33A-2 11A1 33A-5 33A-4 $b^{2}c^{63}$
$D_{11}\times F_7$ 33A2 $33$ $14$ $C_{66}$ 33A4 11A2 33A1 33A8 $b^{2}c^{28}$
$D_{11}\times F_7$ 33A-2 $33$ $14$ $C_{66}$ 33A-4 11A2 33A-1 33A-8 $b^{4}c^{49}$
$D_{11}\times F_7$ 33A4 $33$ $14$ $C_{66}$ 33A8 11A4 33A2 33A-5 $b^{4}c^{56}$
$D_{11}\times F_7$ 33A-4 $33$ $14$ $C_{66}$ 33A-8 11A4 33A-2 33A5 $b^{2}c^{21}$
$D_{11}\times F_7$ 33A5 $33$ $14$ $C_{66}$ 33A1 11A5 33A-8 33A2 $b^{2}c^{70}$
$D_{11}\times F_7$ 33A-5 $33$ $14$ $C_{66}$ 33A-1 11A5 33A8 33A-2 $b^{4}c^{7}$
$D_{11}\times F_7$ 33A8 $33$ $14$ $C_{66}$ 33A-5 11A3 33A4 33A-1 $b^{2}c^{35}$
$D_{11}\times F_7$ 33A-8 $33$ $14$ $C_{66}$ 33A5 11A3 33A-4 33A1 $b^{4}c^{42}$
$D_{11}\times F_7$ 66A1 $66$ $14$ $C_{66}$ 33A1 22A1 66A5 66A7 $ab^{2}c^{7}$
$D_{11}\times F_7$ 66A-1 $66$ $14$ $C_{66}$ 33A-1 22A1 66A-5 66A-7 $ab^{4}c^{7}$
$D_{11}\times F_7$ 66A5 $66$ $14$ $C_{66}$ 33A5 22A5 66A19 66A-13 $ab^{4}c^{2}$
$D_{11}\times F_7$ 66A-5 $66$ $14$ $C_{66}$ 33A-5 22A5 66A-19 66A13 $ab^{2}c^{2}$
$D_{11}\times F_7$ 66A7 $66$ $14$ $C_{66}$ 33A4 22A7 66A-13 66A-5 $ab^{2}c^{28}$
$D_{11}\times F_7$ 66A-7 $66$ $14$ $C_{66}$ 33A-4 22A7 66A13 66A5 $ab^{4}c^{28}$
$D_{11}\times F_7$ 66A13 $66$ $14$ $C_{66}$ 33A-2 22A9 66A-1 66A19 $ab^{2}c^{14}$
$D_{11}\times F_7$ 66A-13 $66$ $14$ $C_{66}$ 33A2 22A9 66A1 66A-19 $ab^{4}c^{14}$
$D_{11}\times F_7$ 66A19 $66$ $14$ $C_{66}$ 33A-8 22A3 66A-7 66A1 $ab^{2}c$
$D_{11}\times F_7$ 66A-19 $66$ $14$ $C_{66}$ 33A8 22A3 66A7 66A-1 $ab^{4}c$
$D_{11}\times F_7$ 77A1 $77$ $12$ $C_{77}$ 77A2 77A3 77A5 11A2 $c$
$D_{11}\times F_7$ 77A2 $77$ $12$ $C_{77}$ 77A4 77A5 77A1 11A4 $c^{2}$
$D_{11}\times F_7$ 77A3 $77$ $12$ $C_{77}$ 77A5 77A2 77A4 11A5 $c^{3}$
$D_{11}\times F_7$ 77A4 $77$ $12$ $C_{77}$ 77A3 77A1 77A2 11A3 $c^{4}$
$D_{11}\times F_7$ 77A5 $77$ $12$ $C_{77}$ 77A1 77A4 77A3 11A1 $c^{5}$
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