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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{8}=c^{77}=[a,c]=1, a^{2}=b^{4}, b^{a}=b^{7}, c^{b}=c^{76} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 7P 11P
$C_{77}:Q_{16}$ 1A $1$ $1$ $C_{77}:Q_{16}$ 1A 1A 1A $1$
$C_{77}:Q_{16}$ 2A $2$ $1$ $C_{77}:Q_{16}$ 1A 2A 2A $b^{4}$
$C_{77}:Q_{16}$ 4A $4$ $2$ $C_{77}:C_8$ 2A 4A 4A $b^{2}$
$C_{77}:Q_{16}$ 4B $4$ $4$ $C_{308}$ 2A 4B 4B $a$
$C_{77}:Q_{16}$ 4C $4$ $308$ $C_4$ 2A 4C 4C $abc^{6}$
$C_{77}:Q_{16}$ 7A1 $7$ $2$ $Q_8\times C_{77}$ 7A2 7A3 7A2 $c^{44}$
$C_{77}:Q_{16}$ 7A2 $7$ $2$ $Q_8\times C_{77}$ 7A3 7A1 7A3 $c^{11}$
$C_{77}:Q_{16}$ 7A3 $7$ $2$ $Q_8\times C_{77}$ 7A1 7A2 7A1 $c^{55}$
$C_{77}:Q_{16}$ 8A1 $8$ $154$ $C_8$ 4A 8A3 8A3 $b^{3}c^{76}$
$C_{77}:Q_{16}$ 8A3 $8$ $154$ $C_8$ 4A 8A1 8A1 $bc^{76}$
$C_{77}:Q_{16}$ 11A1 $11$ $2$ $Q_8\times C_{77}$ 11A2 11A3 11A5 $c^{28}$
$C_{77}:Q_{16}$ 11A2 $11$ $2$ $Q_8\times C_{77}$ 11A4 11A5 11A1 $c^{56}$
$C_{77}:Q_{16}$ 11A3 $11$ $2$ $Q_8\times C_{77}$ 11A5 11A2 11A4 $c^{7}$
$C_{77}:Q_{16}$ 11A4 $11$ $2$ $Q_8\times C_{77}$ 11A3 11A1 11A2 $c^{35}$
$C_{77}:Q_{16}$ 11A5 $11$ $2$ $Q_8\times C_{77}$ 11A1 11A4 11A3 $c^{63}$
$C_{77}:Q_{16}$ 14A1 $14$ $2$ $Q_8\times C_{77}$ 7A1 14A3 14A5 $b^{4}c^{22}$
$C_{77}:Q_{16}$ 14A3 $14$ $2$ $Q_8\times C_{77}$ 7A3 14A5 14A1 $b^{4}c^{66}$
$C_{77}:Q_{16}$ 14A5 $14$ $2$ $Q_8\times C_{77}$ 7A2 14A1 14A3 $b^{4}c^{33}$
$C_{77}:Q_{16}$ 22A1 $22$ $2$ $Q_8\times C_{77}$ 11A1 22A3 22A5 $b^{4}c^{14}$
$C_{77}:Q_{16}$ 22A3 $22$ $2$ $Q_8\times C_{77}$ 11A3 22A9 22A7 $b^{4}c^{42}$
$C_{77}:Q_{16}$ 22A5 $22$ $2$ $Q_8\times C_{77}$ 11A5 22A7 22A3 $b^{4}c^{70}$
$C_{77}:Q_{16}$ 22A7 $22$ $2$ $Q_8\times C_{77}$ 11A4 22A1 22A9 $b^{4}c^{21}$
$C_{77}:Q_{16}$ 22A9 $22$ $2$ $Q_8\times C_{77}$ 11A2 22A5 22A1 $b^{4}c^{49}$
$C_{77}:Q_{16}$ 28A1 $28$ $4$ $C_{308}$ 14A1 28A3 28A5 $b^{6}c^{11}$
$C_{77}:Q_{16}$ 28A3 $28$ $4$ $C_{308}$ 14A3 28A5 28A1 $b^{2}c^{33}$
$C_{77}:Q_{16}$ 28A5 $28$ $4$ $C_{308}$ 14A5 28A1 28A3 $b^{6}c^{55}$
$C_{77}:Q_{16}$ 28B1 $28$ $4$ $C_{308}$ 14A1 28B3 28B5 $ab^{4}c^{11}$
$C_{77}:Q_{16}$ 28B-1 $28$ $4$ $C_{308}$ 14A1 28B-3 28B-5 $ac^{66}$
$C_{77}:Q_{16}$ 28B3 $28$ $4$ $C_{308}$ 14A3 28B-5 28B1 $ac^{33}$
$C_{77}:Q_{16}$ 28B-3 $28$ $4$ $C_{308}$ 14A3 28B5 28B-1 $ab^{4}c^{44}$
$C_{77}:Q_{16}$ 28B5 $28$ $4$ $C_{308}$ 14A5 28B1 28B-3 $ab^{4}c^{55}$
$C_{77}:Q_{16}$ 28B-5 $28$ $4$ $C_{308}$ 14A5 28B-1 28B3 $ac^{22}$
$C_{77}:Q_{16}$ 44A1 $44$ $4$ $C_{308}$ 22A1 44A3 44A5 $b^{6}c^{7}$
$C_{77}:Q_{16}$ 44A3 $44$ $4$ $C_{308}$ 22A3 44A9 44A7 $b^{2}c^{21}$
$C_{77}:Q_{16}$ 44A5 $44$ $4$ $C_{308}$ 22A5 44A7 44A3 $b^{6}c^{35}$
$C_{77}:Q_{16}$ 44A7 $44$ $4$ $C_{308}$ 22A7 44A1 44A9 $b^{2}c^{49}$
$C_{77}:Q_{16}$ 44A9 $44$ $4$ $C_{308}$ 22A9 44A5 44A1 $b^{6}c^{63}$
$C_{77}:Q_{16}$ 44B1 $44$ $4$ $C_{308}$ 22A1 44B3 44B5 $ab^{4}c^{7}$
$C_{77}:Q_{16}$ 44B-1 $44$ $4$ $C_{308}$ 22A1 44B-3 44B-5 $ac^{70}$
$C_{77}:Q_{16}$ 44B3 $44$ $4$ $C_{308}$ 22A3 44B9 44B-7 $ac^{21}$
$C_{77}:Q_{16}$ 44B-3 $44$ $4$ $C_{308}$ 22A3 44B-9 44B7 $ab^{4}c^{56}$
$C_{77}:Q_{16}$ 44B5 $44$ $4$ $C_{308}$ 22A5 44B-7 44B3 $ab^{4}c^{35}$
$C_{77}:Q_{16}$ 44B-5 $44$ $4$ $C_{308}$ 22A5 44B7 44B-3 $ac^{42}$
$C_{77}:Q_{16}$ 44B7 $44$ $4$ $C_{308}$ 22A7 44B-1 44B-9 $ac^{49}$
$C_{77}:Q_{16}$ 44B-7 $44$ $4$ $C_{308}$ 22A7 44B1 44B9 $ab^{4}c^{28}$
$C_{77}:Q_{16}$ 44B9 $44$ $4$ $C_{308}$ 22A9 44B5 44B1 $ab^{4}c^{63}$
$C_{77}:Q_{16}$ 44B-9 $44$ $4$ $C_{308}$ 22A9 44B-5 44B-1 $ac^{14}$
$C_{77}:Q_{16}$ 77A1 $77$ $2$ $Q_8\times C_{77}$ 77A2 77A3 77A5 $c^{4}$
$C_{77}:Q_{16}$ 77A2 $77$ $2$ $Q_8\times C_{77}$ 77A4 77A6 77A10 $c^{8}$
$C_{77}:Q_{16}$ 77A3 $77$ $2$ $Q_8\times C_{77}$ 77A6 77A9 77A15 $c^{12}$
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