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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{2}=b^{136}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 17P
$C_2\times C_{136}$ 1A $1$ $1$ $C_2\times C_{136}$ 1A 1A $1$
$C_2\times C_{136}$ 2A $2$ $1$ $C_2\times C_{136}$ 1A 2A $a$
$C_2\times C_{136}$ 2B $2$ $1$ $C_2\times C_{136}$ 1A 2B $ab^{68}$
$C_2\times C_{136}$ 2C $2$ $1$ $C_2\times C_{136}$ 1A 2C $b^{68}$
$C_2\times C_{136}$ 4A1 $4$ $1$ $C_2\times C_{136}$ 2C 4A1 $ab^{34}$
$C_2\times C_{136}$ 4A-1 $4$ $1$ $C_2\times C_{136}$ 2C 4A-1 $ab^{102}$
$C_2\times C_{136}$ 4B1 $4$ $1$ $C_2\times C_{136}$ 2C 4B1 $b^{34}$
$C_2\times C_{136}$ 4B-1 $4$ $1$ $C_2\times C_{136}$ 2C 4B-1 $b^{102}$
$C_2\times C_{136}$ 8A1 $8$ $1$ $C_2\times C_{136}$ 4B1 8A1 $b^{17}$
$C_2\times C_{136}$ 8A-1 $8$ $1$ $C_2\times C_{136}$ 4B-1 8A-1 $b^{119}$
$C_2\times C_{136}$ 8A3 $8$ $1$ $C_2\times C_{136}$ 4B-1 8A3 $b^{51}$
$C_2\times C_{136}$ 8A-3 $8$ $1$ $C_2\times C_{136}$ 4B1 8A-3 $b^{85}$
$C_2\times C_{136}$ 8B1 $8$ $1$ $C_2\times C_{136}$ 4B1 8B1 $ab^{17}$
$C_2\times C_{136}$ 8B-1 $8$ $1$ $C_2\times C_{136}$ 4B-1 8B-1 $ab^{119}$
$C_2\times C_{136}$ 8B3 $8$ $1$ $C_2\times C_{136}$ 4B-1 8B3 $ab^{51}$
$C_2\times C_{136}$ 8B-3 $8$ $1$ $C_2\times C_{136}$ 4B1 8B-3 $ab^{85}$
$C_2\times C_{136}$ 17A1 $17$ $1$ $C_2\times C_{136}$ 17A2 1A $b^{16}$
$C_2\times C_{136}$ 17A-1 $17$ $1$ $C_2\times C_{136}$ 17A-2 1A $b^{120}$
$C_2\times C_{136}$ 17A2 $17$ $1$ $C_2\times C_{136}$ 17A4 1A $b^{32}$
$C_2\times C_{136}$ 17A-2 $17$ $1$ $C_2\times C_{136}$ 17A-4 1A $b^{104}$
$C_2\times C_{136}$ 17A3 $17$ $1$ $C_2\times C_{136}$ 17A6 1A $b^{48}$
$C_2\times C_{136}$ 17A-3 $17$ $1$ $C_2\times C_{136}$ 17A-6 1A $b^{88}$
$C_2\times C_{136}$ 17A4 $17$ $1$ $C_2\times C_{136}$ 17A8 1A $b^{64}$
$C_2\times C_{136}$ 17A-4 $17$ $1$ $C_2\times C_{136}$ 17A-8 1A $b^{72}$
$C_2\times C_{136}$ 17A5 $17$ $1$ $C_2\times C_{136}$ 17A-7 1A $b^{80}$
$C_2\times C_{136}$ 17A-5 $17$ $1$ $C_2\times C_{136}$ 17A7 1A $b^{56}$
$C_2\times C_{136}$ 17A6 $17$ $1$ $C_2\times C_{136}$ 17A-5 1A $b^{96}$
$C_2\times C_{136}$ 17A-6 $17$ $1$ $C_2\times C_{136}$ 17A5 1A $b^{40}$
$C_2\times C_{136}$ 17A7 $17$ $1$ $C_2\times C_{136}$ 17A-3 1A $b^{112}$
$C_2\times C_{136}$ 17A-7 $17$ $1$ $C_2\times C_{136}$ 17A3 1A $b^{24}$
$C_2\times C_{136}$ 17A8 $17$ $1$ $C_2\times C_{136}$ 17A-1 1A $b^{128}$
$C_2\times C_{136}$ 17A-8 $17$ $1$ $C_2\times C_{136}$ 17A1 1A $b^{8}$
$C_2\times C_{136}$ 34A1 $34$ $1$ $C_2\times C_{136}$ 17A1 2A $ab^{8}$
$C_2\times C_{136}$ 34A-1 $34$ $1$ $C_2\times C_{136}$ 17A-1 2A $ab^{128}$
$C_2\times C_{136}$ 34A3 $34$ $1$ $C_2\times C_{136}$ 17A3 2A $ab^{24}$
$C_2\times C_{136}$ 34A-3 $34$ $1$ $C_2\times C_{136}$ 17A-3 2A $ab^{112}$
$C_2\times C_{136}$ 34A5 $34$ $1$ $C_2\times C_{136}$ 17A5 2A $ab^{40}$
$C_2\times C_{136}$ 34A-5 $34$ $1$ $C_2\times C_{136}$ 17A-5 2A $ab^{96}$
$C_2\times C_{136}$ 34A7 $34$ $1$ $C_2\times C_{136}$ 17A7 2A $ab^{56}$
$C_2\times C_{136}$ 34A-7 $34$ $1$ $C_2\times C_{136}$ 17A-7 2A $ab^{80}$
$C_2\times C_{136}$ 34A9 $34$ $1$ $C_2\times C_{136}$ 17A-8 2A $ab^{72}$
$C_2\times C_{136}$ 34A-9 $34$ $1$ $C_2\times C_{136}$ 17A8 2A $ab^{64}$
$C_2\times C_{136}$ 34A11 $34$ $1$ $C_2\times C_{136}$ 17A-6 2A $ab^{88}$
$C_2\times C_{136}$ 34A-11 $34$ $1$ $C_2\times C_{136}$ 17A6 2A $ab^{48}$
$C_2\times C_{136}$ 34A13 $34$ $1$ $C_2\times C_{136}$ 17A-4 2A $ab^{104}$
$C_2\times C_{136}$ 34A-13 $34$ $1$ $C_2\times C_{136}$ 17A4 2A $ab^{32}$
$C_2\times C_{136}$ 34A15 $34$ $1$ $C_2\times C_{136}$ 17A-2 2A $ab^{120}$
$C_2\times C_{136}$ 34A-15 $34$ $1$ $C_2\times C_{136}$ 17A2 2A $ab^{16}$
$C_2\times C_{136}$ 34B1 $34$ $1$ $C_2\times C_{136}$ 17A-8 2B $ab^{4}$
$C_2\times C_{136}$ 34B-1 $34$ $1$ $C_2\times C_{136}$ 17A8 2B $ab^{132}$
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