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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{16}=c^{34}=[b,c]=1, b^{a}=b^{13}c^{17}, c^{a}=b^{8}c \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 17P
$\OD_{32}:C_{34}$ 1A $1$ $1$ $\OD_{32}:C_{34}$ 1A 1A $1$
$\OD_{32}:C_{34}$ 2A $2$ $1$ $\OD_{32}:C_{34}$ 1A 2A $b^{8}$
$\OD_{32}:C_{34}$ 2B $2$ $2$ $C_2\times C_{272}$ 1A 2B $c^{17}$
$\OD_{32}:C_{34}$ 2C $2$ $4$ $C_2\times C_{136}$ 1A 2C $a$
$\OD_{32}:C_{34}$ 4A1 $4$ $1$ $\OD_{32}:C_{34}$ 2A 4A1 $b^{12}$
$\OD_{32}:C_{34}$ 4A-1 $4$ $1$ $\OD_{32}:C_{34}$ 2A 4A-1 $b^{4}$
$\OD_{32}:C_{34}$ 4B $4$ $2$ $C_2\times C_{272}$ 2A 4B $b^{4}c^{17}$
$\OD_{32}:C_{34}$ 4C $4$ $4$ $C_2\times C_{136}$ 2A 4C $ac^{17}$
$\OD_{32}:C_{34}$ 8A1 $8$ $1$ $\OD_{32}:C_{34}$ 4A1 8A1 $b^{14}c^{17}$
$\OD_{32}:C_{34}$ 8A-1 $8$ $1$ $\OD_{32}:C_{34}$ 4A-1 8A-1 $b^{2}c^{17}$
$\OD_{32}:C_{34}$ 8A3 $8$ $1$ $\OD_{32}:C_{34}$ 4A-1 8A3 $b^{10}c^{17}$
$\OD_{32}:C_{34}$ 8A-3 $8$ $1$ $\OD_{32}:C_{34}$ 4A1 8A-3 $b^{6}c^{17}$
$\OD_{32}:C_{34}$ 8B1 $8$ $2$ $C_2\times C_{272}$ 4A-1 8B1 $b^{2}$
$\OD_{32}:C_{34}$ 8B-1 $8$ $2$ $C_2\times C_{272}$ 4A1 8B-1 $b^{14}$
$\OD_{32}:C_{34}$ 8C1 $8$ $4$ $C_2\times C_{136}$ 4A1 8C1 $ab^{2}$
$\OD_{32}:C_{34}$ 8C-1 $8$ $4$ $C_2\times C_{136}$ 4A-1 8C-1 $ab^{6}$
$\OD_{32}:C_{34}$ 16A1 $16$ $2$ $C_2\times C_{272}$ 8B1 16A1 $b$
$\OD_{32}:C_{34}$ 16A-1 $16$ $2$ $C_2\times C_{272}$ 8B-1 16A-1 $b^{15}$
$\OD_{32}:C_{34}$ 16A3 $16$ $2$ $C_2\times C_{272}$ 8B-1 16A3 $b^{3}$
$\OD_{32}:C_{34}$ 16A-3 $16$ $2$ $C_2\times C_{272}$ 8B1 16A-3 $b^{13}$
$\OD_{32}:C_{34}$ 16A5 $16$ $2$ $C_2\times C_{272}$ 8B1 16A5 $b^{5}$
$\OD_{32}:C_{34}$ 16A-5 $16$ $2$ $C_2\times C_{272}$ 8B-1 16A-5 $b^{11}$
$\OD_{32}:C_{34}$ 16A7 $16$ $2$ $C_2\times C_{272}$ 8B-1 16A7 $b^{7}$
$\OD_{32}:C_{34}$ 16A-7 $16$ $2$ $C_2\times C_{272}$ 8B1 16A-7 $b^{9}$
$\OD_{32}:C_{34}$ 16B1 $16$ $4$ $C_{272}$ 8A1 16B1 $ab$
$\OD_{32}:C_{34}$ 16B-1 $16$ $4$ $C_{272}$ 8A-1 16B-1 $ab^{3}c^{17}$
$\OD_{32}:C_{34}$ 16B3 $16$ $4$ $C_{272}$ 8A3 16B3 $ab^{15}c^{17}$
$\OD_{32}:C_{34}$ 16B-3 $16$ $4$ $C_{272}$ 8A-3 16B-3 $ab^{5}$
$\OD_{32}:C_{34}$ 17A1 $17$ $1$ $\OD_{32}:C_{34}$ 17A2 1A $c^{2}$
$\OD_{32}:C_{34}$ 17A-1 $17$ $1$ $\OD_{32}:C_{34}$ 17A-2 1A $c^{32}$
$\OD_{32}:C_{34}$ 17A2 $17$ $1$ $\OD_{32}:C_{34}$ 17A4 1A $c^{4}$
$\OD_{32}:C_{34}$ 17A-2 $17$ $1$ $\OD_{32}:C_{34}$ 17A-4 1A $c^{30}$
$\OD_{32}:C_{34}$ 17A3 $17$ $1$ $\OD_{32}:C_{34}$ 17A6 1A $c^{6}$
$\OD_{32}:C_{34}$ 17A-3 $17$ $1$ $\OD_{32}:C_{34}$ 17A-6 1A $c^{28}$
$\OD_{32}:C_{34}$ 17A4 $17$ $1$ $\OD_{32}:C_{34}$ 17A8 1A $c^{8}$
$\OD_{32}:C_{34}$ 17A-4 $17$ $1$ $\OD_{32}:C_{34}$ 17A-8 1A $c^{26}$
$\OD_{32}:C_{34}$ 17A5 $17$ $1$ $\OD_{32}:C_{34}$ 17A-7 1A $c^{10}$
$\OD_{32}:C_{34}$ 17A-5 $17$ $1$ $\OD_{32}:C_{34}$ 17A7 1A $c^{24}$
$\OD_{32}:C_{34}$ 17A6 $17$ $1$ $\OD_{32}:C_{34}$ 17A-5 1A $c^{12}$
$\OD_{32}:C_{34}$ 17A-6 $17$ $1$ $\OD_{32}:C_{34}$ 17A5 1A $c^{22}$
$\OD_{32}:C_{34}$ 17A7 $17$ $1$ $\OD_{32}:C_{34}$ 17A-3 1A $c^{14}$
$\OD_{32}:C_{34}$ 17A-7 $17$ $1$ $\OD_{32}:C_{34}$ 17A3 1A $c^{20}$
$\OD_{32}:C_{34}$ 17A8 $17$ $1$ $\OD_{32}:C_{34}$ 17A-1 1A $c^{16}$
$\OD_{32}:C_{34}$ 17A-8 $17$ $1$ $\OD_{32}:C_{34}$ 17A1 1A $c^{18}$
$\OD_{32}:C_{34}$ 34A1 $34$ $1$ $\OD_{32}:C_{34}$ 17A2 2A $b^{8}c^{2}$
$\OD_{32}:C_{34}$ 34A-1 $34$ $1$ $\OD_{32}:C_{34}$ 17A-2 2A $b^{8}c^{32}$
$\OD_{32}:C_{34}$ 34A3 $34$ $1$ $\OD_{32}:C_{34}$ 17A6 2A $b^{8}c^{6}$
$\OD_{32}:C_{34}$ 34A-3 $34$ $1$ $\OD_{32}:C_{34}$ 17A-6 2A $b^{8}c^{28}$
$\OD_{32}:C_{34}$ 34A5 $34$ $1$ $\OD_{32}:C_{34}$ 17A-7 2A $b^{8}c^{10}$
$\OD_{32}:C_{34}$ 34A-5 $34$ $1$ $\OD_{32}:C_{34}$ 17A7 2A $b^{8}c^{24}$
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