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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{4}=c^{136}=[b,c]=1, b^{a}=bc^{68}, c^{a}=b^{2}c \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 17P
$(C_4\times C_8):C_{34}$ 1A $1$ $1$ $(C_4\times C_8):C_{34}$ 1A 1A $1$
$(C_4\times C_8):C_{34}$ 2A $2$ $1$ $(C_4\times C_8):C_{34}$ 1A 2A $b^{2}$
$(C_4\times C_8):C_{34}$ 2B $2$ $1$ $(C_4\times C_8):C_{34}$ 1A 2B $b^{2}c^{68}$
$(C_4\times C_8):C_{34}$ 2C $2$ $1$ $(C_4\times C_8):C_{34}$ 1A 2C $c^{68}$
$(C_4\times C_8):C_{34}$ 2D $2$ $4$ $C_2^2\times C_{68}$ 1A 2D $a$
$(C_4\times C_8):C_{34}$ 4A1 $4$ $1$ $(C_4\times C_8):C_{34}$ 2C 4A1 $c^{34}$
$(C_4\times C_8):C_{34}$ 4A-1 $4$ $1$ $(C_4\times C_8):C_{34}$ 2C 4A-1 $c^{102}$
$(C_4\times C_8):C_{34}$ 4B1 $4$ $1$ $(C_4\times C_8):C_{34}$ 2C 4B1 $b^{2}c^{34}$
$(C_4\times C_8):C_{34}$ 4B-1 $4$ $1$ $(C_4\times C_8):C_{34}$ 2C 4B-1 $b^{2}c^{102}$
$(C_4\times C_8):C_{34}$ 4C1 $4$ $2$ $C_4\times C_{136}$ 2A 4C1 $b$
$(C_4\times C_8):C_{34}$ 4C-1 $4$ $2$ $C_4\times C_{136}$ 2A 4C-1 $b^{3}$
$(C_4\times C_8):C_{34}$ 4D1 $4$ $2$ $C_4\times C_{136}$ 2B 4D1 $bc^{34}$
$(C_4\times C_8):C_{34}$ 4D-1 $4$ $2$ $C_4\times C_{136}$ 2B 4D-1 $b^{3}c^{102}$
$(C_4\times C_8):C_{34}$ 4E $4$ $4$ $C_2^2\times C_{68}$ 2C 4E $ac^{34}$
$(C_4\times C_8):C_{34}$ 4F $4$ $4$ $C_4\times C_{68}$ 2B 4F $ab$
$(C_4\times C_8):C_{34}$ 4G $4$ $4$ $C_4\times C_{68}$ 2A 4G $abc^{34}$
$(C_4\times C_8):C_{34}$ 8A1 $8$ $2$ $C_4\times C_{136}$ 4A1 8A1 $c^{17}$
$(C_4\times C_8):C_{34}$ 8A-1 $8$ $2$ $C_4\times C_{136}$ 4A-1 8A-1 $c^{119}$
$(C_4\times C_8):C_{34}$ 8A3 $8$ $2$ $C_4\times C_{136}$ 4A-1 8A3 $c^{51}$
$(C_4\times C_8):C_{34}$ 8A-3 $8$ $2$ $C_4\times C_{136}$ 4A1 8A-3 $c^{85}$
$(C_4\times C_8):C_{34}$ 8B1 $8$ $2$ $C_4\times C_{136}$ 4B1 8B1 $bc^{17}$
$(C_4\times C_8):C_{34}$ 8B-1 $8$ $2$ $C_4\times C_{136}$ 4B-1 8B-1 $b^{3}c^{119}$
$(C_4\times C_8):C_{34}$ 8B3 $8$ $2$ $C_4\times C_{136}$ 4B-1 8B3 $b^{3}c^{51}$
$(C_4\times C_8):C_{34}$ 8B-3 $8$ $2$ $C_4\times C_{136}$ 4B1 8B-3 $bc^{85}$
$(C_4\times C_8):C_{34}$ 8C1 $8$ $4$ $C_2\times C_{136}$ 4B1 8C1 $ac^{17}$
$(C_4\times C_8):C_{34}$ 8C-1 $8$ $4$ $C_2\times C_{136}$ 4B-1 8C-1 $ab^{2}c^{119}$
$(C_4\times C_8):C_{34}$ 8D1 $8$ $4$ $C_2\times C_{136}$ 4A-1 8D1 $abc^{17}$
$(C_4\times C_8):C_{34}$ 8D-1 $8$ $4$ $C_2\times C_{136}$ 4A1 8D-1 $abc^{51}$
$(C_4\times C_8):C_{34}$ 17A1 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A2 1A $c^{16}$
$(C_4\times C_8):C_{34}$ 17A-1 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-2 1A $c^{120}$
$(C_4\times C_8):C_{34}$ 17A2 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A4 1A $c^{32}$
$(C_4\times C_8):C_{34}$ 17A-2 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-4 1A $c^{104}$
$(C_4\times C_8):C_{34}$ 17A3 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A6 1A $c^{48}$
$(C_4\times C_8):C_{34}$ 17A-3 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-6 1A $c^{88}$
$(C_4\times C_8):C_{34}$ 17A4 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A8 1A $c^{64}$
$(C_4\times C_8):C_{34}$ 17A-4 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-8 1A $c^{72}$
$(C_4\times C_8):C_{34}$ 17A5 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-7 1A $c^{80}$
$(C_4\times C_8):C_{34}$ 17A-5 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A7 1A $c^{56}$
$(C_4\times C_8):C_{34}$ 17A6 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-5 1A $c^{96}$
$(C_4\times C_8):C_{34}$ 17A-6 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A5 1A $c^{40}$
$(C_4\times C_8):C_{34}$ 17A7 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-3 1A $c^{112}$
$(C_4\times C_8):C_{34}$ 17A-7 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A3 1A $c^{24}$
$(C_4\times C_8):C_{34}$ 17A8 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A-1 1A $c^{128}$
$(C_4\times C_8):C_{34}$ 17A-8 $17$ $1$ $(C_4\times C_8):C_{34}$ 17A1 1A $c^{8}$
$(C_4\times C_8):C_{34}$ 34A1 $34$ $1$ $(C_4\times C_8):C_{34}$ 17A2 2A $b^{2}c^{16}$
$(C_4\times C_8):C_{34}$ 34A-1 $34$ $1$ $(C_4\times C_8):C_{34}$ 17A-2 2A $b^{2}c^{120}$
$(C_4\times C_8):C_{34}$ 34A3 $34$ $1$ $(C_4\times C_8):C_{34}$ 17A6 2A $b^{2}c^{48}$
$(C_4\times C_8):C_{34}$ 34A-3 $34$ $1$ $(C_4\times C_8):C_{34}$ 17A-6 2A $b^{2}c^{88}$
$(C_4\times C_8):C_{34}$ 34A5 $34$ $1$ $(C_4\times C_8):C_{34}$ 17A-7 2A $b^{2}c^{80}$
$(C_4\times C_8):C_{34}$ 34A-5 $34$ $1$ $(C_4\times C_8):C_{34}$ 17A7 2A $b^{2}c^{56}$
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