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

Group Label Order Size Centralizer Powers Representative
2P 17P
$C_{136}$ 1A $1$ $1$ $C_{136}$ 1A 1A $1$
$C_{136}$ 2A $2$ $1$ $C_{136}$ 1A 2A $a^{68}$
$C_{136}$ 4A1 $4$ $1$ $C_{136}$ 2A 4A1 $a^{34}$
$C_{136}$ 4A-1 $4$ $1$ $C_{136}$ 2A 4A-1 $a^{102}$
$C_{136}$ 8A1 $8$ $1$ $C_{136}$ 4A1 8A1 $a^{17}$
$C_{136}$ 8A-1 $8$ $1$ $C_{136}$ 4A-1 8A-1 $a^{119}$
$C_{136}$ 8A3 $8$ $1$ $C_{136}$ 4A-1 8A3 $a^{51}$
$C_{136}$ 8A-3 $8$ $1$ $C_{136}$ 4A1 8A-3 $a^{85}$
$C_{136}$ 17A1 $17$ $1$ $C_{136}$ 17A2 1A $a^{8}$
$C_{136}$ 17A-1 $17$ $1$ $C_{136}$ 17A-2 1A $a^{128}$
$C_{136}$ 17A2 $17$ $1$ $C_{136}$ 17A4 1A $a^{16}$
$C_{136}$ 17A-2 $17$ $1$ $C_{136}$ 17A-4 1A $a^{120}$
$C_{136}$ 17A3 $17$ $1$ $C_{136}$ 17A6 1A $a^{24}$
$C_{136}$ 17A-3 $17$ $1$ $C_{136}$ 17A-6 1A $a^{112}$
$C_{136}$ 17A4 $17$ $1$ $C_{136}$ 17A8 1A $a^{32}$
$C_{136}$ 17A-4 $17$ $1$ $C_{136}$ 17A-8 1A $a^{104}$
$C_{136}$ 17A5 $17$ $1$ $C_{136}$ 17A-7 1A $a^{40}$
$C_{136}$ 17A-5 $17$ $1$ $C_{136}$ 17A7 1A $a^{96}$
$C_{136}$ 17A6 $17$ $1$ $C_{136}$ 17A-5 1A $a^{48}$
$C_{136}$ 17A-6 $17$ $1$ $C_{136}$ 17A5 1A $a^{88}$
$C_{136}$ 17A7 $17$ $1$ $C_{136}$ 17A-3 1A $a^{56}$
$C_{136}$ 17A-7 $17$ $1$ $C_{136}$ 17A3 1A $a^{80}$
$C_{136}$ 17A8 $17$ $1$ $C_{136}$ 17A-1 1A $a^{64}$
$C_{136}$ 17A-8 $17$ $1$ $C_{136}$ 17A1 1A $a^{72}$
$C_{136}$ 34A1 $34$ $1$ $C_{136}$ 17A1 2A $a^{4}$
$C_{136}$ 34A-1 $34$ $1$ $C_{136}$ 17A-1 2A $a^{132}$
$C_{136}$ 34A3 $34$ $1$ $C_{136}$ 17A3 2A $a^{12}$
$C_{136}$ 34A-3 $34$ $1$ $C_{136}$ 17A-3 2A $a^{124}$
$C_{136}$ 34A5 $34$ $1$ $C_{136}$ 17A5 2A $a^{20}$
$C_{136}$ 34A-5 $34$ $1$ $C_{136}$ 17A-5 2A $a^{116}$
$C_{136}$ 34A7 $34$ $1$ $C_{136}$ 17A7 2A $a^{28}$
$C_{136}$ 34A-7 $34$ $1$ $C_{136}$ 17A-7 2A $a^{108}$
$C_{136}$ 34A9 $34$ $1$ $C_{136}$ 17A-8 2A $a^{36}$
$C_{136}$ 34A-9 $34$ $1$ $C_{136}$ 17A8 2A $a^{100}$
$C_{136}$ 34A11 $34$ $1$ $C_{136}$ 17A-6 2A $a^{44}$
$C_{136}$ 34A-11 $34$ $1$ $C_{136}$ 17A6 2A $a^{92}$
$C_{136}$ 34A13 $34$ $1$ $C_{136}$ 17A-4 2A $a^{52}$
$C_{136}$ 34A-13 $34$ $1$ $C_{136}$ 17A4 2A $a^{84}$
$C_{136}$ 34A15 $34$ $1$ $C_{136}$ 17A-2 2A $a^{60}$
$C_{136}$ 34A-15 $34$ $1$ $C_{136}$ 17A2 2A $a^{76}$
$C_{136}$ 68A1 $68$ $1$ $C_{136}$ 34A1 4A1 $a^{2}$
$C_{136}$ 68A-1 $68$ $1$ $C_{136}$ 34A-1 4A-1 $a^{134}$
$C_{136}$ 68A3 $68$ $1$ $C_{136}$ 34A3 4A-1 $a^{6}$
$C_{136}$ 68A-3 $68$ $1$ $C_{136}$ 34A-3 4A1 $a^{130}$
$C_{136}$ 68A5 $68$ $1$ $C_{136}$ 34A5 4A1 $a^{10}$
$C_{136}$ 68A-5 $68$ $1$ $C_{136}$ 34A-5 4A-1 $a^{126}$
$C_{136}$ 68A7 $68$ $1$ $C_{136}$ 34A7 4A-1 $a^{14}$
$C_{136}$ 68A-7 $68$ $1$ $C_{136}$ 34A-7 4A1 $a^{122}$
$C_{136}$ 68A9 $68$ $1$ $C_{136}$ 34A9 4A1 $a^{18}$
$C_{136}$ 68A-9 $68$ $1$ $C_{136}$ 34A-9 4A-1 $a^{118}$
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