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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{8}=b^{105}=1, b^{a}=b^{34} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P 7P
$C_{105}:C_8$ 1A $1$ $1$ $C_{105}:C_8$ 1A 1A 1A 1A $1$
$C_{105}:C_8$ 2A $2$ $1$ $C_{105}:C_8$ 1A 2A 2A 2A $a^{4}$
$C_{105}:C_8$ 3A1 $3$ $1$ $C_{105}:C_8$ 3A-1 1A 3A-1 3A1 $b^{35}$
$C_{105}:C_8$ 3A-1 $3$ $1$ $C_{105}:C_8$ 3A1 1A 3A1 3A-1 $b^{70}$
$C_{105}:C_8$ 4A1 $4$ $1$ $C_{105}:C_8$ 2A 4A-1 4A1 4A-1 $a^{2}$
$C_{105}:C_8$ 4A-1 $4$ $1$ $C_{105}:C_8$ 2A 4A1 4A-1 4A1 $a^{6}$
$C_{105}:C_8$ 5A1 $5$ $2$ $C_{420}$ 5A2 5A2 1A 5A2 $b^{84}$
$C_{105}:C_8$ 5A2 $5$ $2$ $C_{420}$ 5A1 5A1 1A 5A1 $b^{63}$
$C_{105}:C_8$ 6A1 $6$ $1$ $C_{105}:C_8$ 3A1 2A 6A-1 6A1 $a^{4}b^{70}$
$C_{105}:C_8$ 6A-1 $6$ $1$ $C_{105}:C_8$ 3A-1 2A 6A1 6A-1 $a^{4}b^{35}$
$C_{105}:C_8$ 7A1 $7$ $2$ $C_{420}$ 7A2 7A3 7A2 1A $b^{60}$
$C_{105}:C_8$ 7A2 $7$ $2$ $C_{420}$ 7A3 7A1 7A3 1A $b^{15}$
$C_{105}:C_8$ 7A3 $7$ $2$ $C_{420}$ 7A1 7A2 7A1 1A $b^{75}$
$C_{105}:C_8$ 8A1 $8$ $35$ $C_{24}$ 4A1 8A3 8A-3 8A-1 $ab^{90}$
$C_{105}:C_8$ 8A-1 $8$ $35$ $C_{24}$ 4A-1 8A-3 8A3 8A1 $a^{7}b^{90}$
$C_{105}:C_8$ 8A3 $8$ $35$ $C_{24}$ 4A-1 8A1 8A-1 8A-3 $a^{3}b^{90}$
$C_{105}:C_8$ 8A-3 $8$ $35$ $C_{24}$ 4A1 8A-1 8A1 8A3 $a^{5}b^{90}$
$C_{105}:C_8$ 10A1 $10$ $2$ $C_{420}$ 5A1 10A3 2A 10A3 $a^{4}b^{42}$
$C_{105}:C_8$ 10A3 $10$ $2$ $C_{420}$ 5A2 10A1 2A 10A1 $a^{4}b^{21}$
$C_{105}:C_8$ 12A1 $12$ $1$ $C_{105}:C_8$ 6A1 4A1 12A5 12A-5 $a^{6}b^{35}$
$C_{105}:C_8$ 12A-1 $12$ $1$ $C_{105}:C_8$ 6A-1 4A-1 12A-5 12A5 $a^{2}b^{70}$
$C_{105}:C_8$ 12A5 $12$ $1$ $C_{105}:C_8$ 6A-1 4A1 12A1 12A-1 $a^{6}b^{70}$
$C_{105}:C_8$ 12A-5 $12$ $1$ $C_{105}:C_8$ 6A1 4A-1 12A-1 12A1 $a^{2}b^{35}$
$C_{105}:C_8$ 14A1 $14$ $2$ $C_{420}$ 7A1 14A3 14A5 2A $a^{4}b^{30}$
$C_{105}:C_8$ 14A3 $14$ $2$ $C_{420}$ 7A3 14A5 14A1 2A $a^{4}b^{90}$
$C_{105}:C_8$ 14A5 $14$ $2$ $C_{420}$ 7A2 14A1 14A3 2A $a^{4}b^{45}$
$C_{105}:C_8$ 15A1 $15$ $2$ $C_{420}$ 15A2 5A1 3A1 15A-2 $b^{28}$
$C_{105}:C_8$ 15A-1 $15$ $2$ $C_{420}$ 15A-2 5A1 3A-1 15A2 $b^{77}$
$C_{105}:C_8$ 15A2 $15$ $2$ $C_{420}$ 15A1 5A2 3A-1 15A-1 $b^{56}$
$C_{105}:C_8$ 15A-2 $15$ $2$ $C_{420}$ 15A-1 5A2 3A1 15A1 $b^{49}$
$C_{105}:C_8$ 20A1 $20$ $2$ $C_{420}$ 10A1 20A3 4A1 20A3 $a^{2}b^{21}$
$C_{105}:C_8$ 20A-1 $20$ $2$ $C_{420}$ 10A1 20A-3 4A-1 20A-3 $a^{6}b^{84}$
$C_{105}:C_8$ 20A3 $20$ $2$ $C_{420}$ 10A3 20A1 4A-1 20A1 $a^{6}b^{63}$
$C_{105}:C_8$ 20A-3 $20$ $2$ $C_{420}$ 10A3 20A-1 4A1 20A-1 $a^{2}b^{42}$
$C_{105}:C_8$ 21A1 $21$ $2$ $C_{420}$ 21A2 7A1 21A2 3A1 $b^{20}$
$C_{105}:C_8$ 21A-1 $21$ $2$ $C_{420}$ 21A-2 7A1 21A-2 3A-1 $b^{85}$
$C_{105}:C_8$ 21A2 $21$ $2$ $C_{420}$ 21A4 7A2 21A4 3A-1 $b^{40}$
$C_{105}:C_8$ 21A-2 $21$ $2$ $C_{420}$ 21A-4 7A2 21A-4 3A1 $b^{65}$
$C_{105}:C_8$ 21A4 $21$ $2$ $C_{420}$ 21A-1 7A3 21A-1 3A1 $b^{80}$
$C_{105}:C_8$ 21A-4 $21$ $2$ $C_{420}$ 21A1 7A3 21A1 3A-1 $b^{25}$
$C_{105}:C_8$ 24A1 $24$ $35$ $C_{24}$ 12A5 8A1 24A5 24A7 $a^{3}b^{20}$
$C_{105}:C_8$ 24A-1 $24$ $35$ $C_{24}$ 12A-5 8A-1 24A-5 24A-7 $a^{5}b^{55}$
$C_{105}:C_8$ 24A5 $24$ $35$ $C_{24}$ 12A1 8A-3 24A1 24A11 $a^{7}b^{55}$
$C_{105}:C_8$ 24A-5 $24$ $35$ $C_{24}$ 12A-1 8A3 24A-1 24A-11 $ab^{20}$
$C_{105}:C_8$ 24A7 $24$ $35$ $C_{24}$ 12A-1 8A-1 24A11 24A1 $a^{5}b^{20}$
$C_{105}:C_8$ 24A-7 $24$ $35$ $C_{24}$ 12A1 8A1 24A-11 24A-1 $a^{3}b^{55}$
$C_{105}:C_8$ 24A11 $24$ $35$ $C_{24}$ 12A-5 8A3 24A7 24A5 $ab^{55}$
$C_{105}:C_8$ 24A-11 $24$ $35$ $C_{24}$ 12A5 8A-3 24A-7 24A-5 $a^{7}b^{20}$
$C_{105}:C_8$ 28A1 $28$ $2$ $C_{420}$ 14A1 28A3 28A5 4A1 $a^{6}b^{15}$
$C_{105}:C_8$ 28A-1 $28$ $2$ $C_{420}$ 14A1 28A-3 28A-5 4A-1 $a^{2}b^{90}$
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