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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{4}=c^{64}=1, b^{a}=bc^{47}, c^{a}=c^{63}, c^{b}=c^{31} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P
$D_{64}:C_4$ 1A $1$ $1$ $D_{64}:C_4$ 1A $1$
$D_{64}:C_4$ 2A $2$ $1$ $D_{64}:C_4$ 1A $c^{32}$
$D_{64}:C_4$ 2B $2$ $2$ $C_{64}:C_4$ 1A $b^{2}c^{32}$
$D_{64}:C_4$ 2C $2$ $64$ $C_2\times C_4$ 1A $ac^{17}$
$D_{64}:C_4$ 4A $4$ $2$ $D_{64}:C_2$ 2A $b^{2}c^{16}$
$D_{64}:C_4$ 4B $4$ $2$ $\OD_{256}$ 2A $c^{16}$
$D_{64}:C_4$ 4C $4$ $64$ $C_2\times C_4$ 2A $ab^{2}c^{51}$
$D_{64}:C_4$ 4D1 $4$ $64$ $C_2\times C_4$ 2B $bc^{15}$
$D_{64}:C_4$ 4D-1 $4$ $64$ $C_2\times C_4$ 2B $b^{3}c^{47}$
$D_{64}:C_4$ 8A1 $8$ $2$ $\OD_{256}$ 4B $c^{8}$
$D_{64}:C_4$ 8A3 $8$ $2$ $\OD_{256}$ 4B $c^{24}$
$D_{64}:C_4$ 8B $8$ $4$ $C_2\times C_{64}$ 4B $b^{2}c^{8}$
$D_{64}:C_4$ 16A1 $16$ $2$ $\OD_{256}$ 8A1 $c^{4}$
$D_{64}:C_4$ 16A3 $16$ $2$ $\OD_{256}$ 8A3 $c^{12}$
$D_{64}:C_4$ 16A5 $16$ $2$ $\OD_{256}$ 8A3 $c^{20}$
$D_{64}:C_4$ 16A7 $16$ $2$ $\OD_{256}$ 8A1 $c^{28}$
$D_{64}:C_4$ 16B1 $16$ $4$ $C_2\times C_{64}$ 8A1 $b^{2}c^{4}$
$D_{64}:C_4$ 16B3 $16$ $4$ $C_2\times C_{64}$ 8A3 $b^{2}c^{20}$
$D_{64}:C_4$ 32A1 $32$ $2$ $\OD_{256}$ 16A1 $c^{2}$
$D_{64}:C_4$ 32A3 $32$ $2$ $\OD_{256}$ 16A3 $c^{6}$
$D_{64}:C_4$ 32A5 $32$ $2$ $\OD_{256}$ 16A5 $c^{10}$
$D_{64}:C_4$ 32A7 $32$ $2$ $\OD_{256}$ 16A7 $c^{14}$
$D_{64}:C_4$ 32A9 $32$ $2$ $\OD_{256}$ 16A7 $c^{18}$
$D_{64}:C_4$ 32A11 $32$ $2$ $\OD_{256}$ 16A5 $c^{22}$
$D_{64}:C_4$ 32A13 $32$ $2$ $\OD_{256}$ 16A3 $c^{26}$
$D_{64}:C_4$ 32A15 $32$ $2$ $\OD_{256}$ 16A1 $c^{30}$
$D_{64}:C_4$ 32B1 $32$ $4$ $C_2\times C_{64}$ 16A1 $b^{2}c^{2}$
$D_{64}:C_4$ 32B3 $32$ $4$ $C_2\times C_{64}$ 16A3 $b^{2}c^{6}$
$D_{64}:C_4$ 32B5 $32$ $4$ $C_2\times C_{64}$ 16A5 $b^{2}c^{10}$
$D_{64}:C_4$ 32B7 $32$ $4$ $C_2\times C_{64}$ 16A7 $b^{2}c^{18}$
$D_{64}:C_4$ 64A1 $64$ $2$ $\OD_{256}$ 32A15 $b^{2}c^{49}$
$D_{64}:C_4$ 64A-1 $64$ $2$ $\OD_{256}$ 32A15 $b^{2}c^{15}$
$D_{64}:C_4$ 64A3 $64$ $2$ $\OD_{256}$ 32A13 $b^{2}c^{19}$
$D_{64}:C_4$ 64A-3 $64$ $2$ $\OD_{256}$ 32A13 $b^{2}c^{45}$
$D_{64}:C_4$ 64A5 $64$ $2$ $\OD_{256}$ 32A11 $b^{2}c^{53}$
$D_{64}:C_4$ 64A-5 $64$ $2$ $\OD_{256}$ 32A11 $b^{2}c^{11}$
$D_{64}:C_4$ 64A7 $64$ $2$ $\OD_{256}$ 32A9 $b^{2}c^{23}$
$D_{64}:C_4$ 64A-7 $64$ $2$ $\OD_{256}$ 32A9 $b^{2}c^{41}$
$D_{64}:C_4$ 64A9 $64$ $2$ $\OD_{256}$ 32A7 $b^{2}c^{57}$
$D_{64}:C_4$ 64A-9 $64$ $2$ $\OD_{256}$ 32A7 $b^{2}c^{7}$
$D_{64}:C_4$ 64A11 $64$ $2$ $\OD_{256}$ 32A5 $b^{2}c^{27}$
$D_{64}:C_4$ 64A-11 $64$ $2$ $\OD_{256}$ 32A5 $b^{2}c^{37}$
$D_{64}:C_4$ 64A13 $64$ $2$ $\OD_{256}$ 32A3 $b^{2}c^{61}$
$D_{64}:C_4$ 64A-13 $64$ $2$ $\OD_{256}$ 32A3 $b^{2}c^{3}$
$D_{64}:C_4$ 64A15 $64$ $2$ $\OD_{256}$ 32A1 $b^{2}c^{31}$
$D_{64}:C_4$ 64A-15 $64$ $2$ $\OD_{256}$ 32A1 $b^{2}c^{33}$
$D_{64}:C_4$ 64B1 $64$ $4$ $C_2\times C_{64}$ 32A1 $c$
$D_{64}:C_4$ 64B3 $64$ $4$ $C_2\times C_{64}$ 32A3 $c^{3}$
$D_{64}:C_4$ 64B5 $64$ $4$ $C_2\times C_{64}$ 32A5 $c^{5}$
$D_{64}:C_4$ 64B7 $64$ $4$ $C_2\times C_{64}$ 32A7 $c^{25}$
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