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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{5}=c^{70}=[b,c]=1, b^{a}=b^{4}, c^{a}=c^{69} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 7P
$C_5:D_{70}$ 1A $1$ $1$ $C_5:D_{70}$ 1A 1A 1A $1$
$C_5:D_{70}$ 2A $2$ $1$ $C_5:D_{70}$ 1A 2A 2A $c^{35}$
$C_5:D_{70}$ 2B $2$ $175$ $C_2^2$ 1A 2B 2B $abc^{58}$
$C_5:D_{70}$ 2C $2$ $175$ $C_2^2$ 1A 2C 2C $ab^{4}c^{55}$
$C_5:D_{70}$ 5A1 $5$ $2$ $C_5\times C_{70}$ 5A2 5A2 1A $c^{14}$
$C_5:D_{70}$ 5A2 $5$ $2$ $C_5\times C_{70}$ 5A1 5A1 1A $c^{28}$
$C_5:D_{70}$ 5B1 $5$ $2$ $C_5\times C_{70}$ 5B2 5B2 1A $b^{4}c^{14}$
$C_5:D_{70}$ 5B2 $5$ $2$ $C_5\times C_{70}$ 5B1 5B1 1A $b^{3}c^{28}$
$C_5:D_{70}$ 5C1 $5$ $2$ $C_5\times C_{70}$ 5C2 5C2 1A $b^{3}c^{14}$
$C_5:D_{70}$ 5C2 $5$ $2$ $C_5\times C_{70}$ 5C1 5C1 1A $bc^{28}$
$C_5:D_{70}$ 5D1 $5$ $2$ $C_5\times C_{70}$ 5D2 5D2 1A $b^{2}c^{14}$
$C_5:D_{70}$ 5D2 $5$ $2$ $C_5\times C_{70}$ 5D1 5D1 1A $b^{4}c^{28}$
$C_5:D_{70}$ 5E1 $5$ $2$ $C_5\times C_{70}$ 5E2 5E2 1A $bc^{14}$
$C_5:D_{70}$ 5E2 $5$ $2$ $C_5\times C_{70}$ 5E1 5E1 1A $b^{2}c^{28}$
$C_5:D_{70}$ 5F1 $5$ $2$ $C_5\times C_{70}$ 5F2 5F2 1A $b^{4}$
$C_5:D_{70}$ 5F2 $5$ $2$ $C_5\times C_{70}$ 5F1 5F1 1A $b^{3}$
$C_5:D_{70}$ 7A1 $7$ $2$ $C_5\times C_{70}$ 7A2 7A3 7A2 $c^{10}$
$C_5:D_{70}$ 7A2 $7$ $2$ $C_5\times C_{70}$ 7A3 7A1 7A3 $c^{20}$
$C_5:D_{70}$ 7A3 $7$ $2$ $C_5\times C_{70}$ 7A1 7A2 7A1 $c^{30}$
$C_5:D_{70}$ 10A1 $10$ $2$ $C_5\times C_{70}$ 5A1 10A3 2A $c^{7}$
$C_5:D_{70}$ 10A3 $10$ $2$ $C_5\times C_{70}$ 5A2 10A1 2A $c^{21}$
$C_5:D_{70}$ 10B1 $10$ $2$ $C_5\times C_{70}$ 5B1 10B3 2A $b^{2}c^{7}$
$C_5:D_{70}$ 10B3 $10$ $2$ $C_5\times C_{70}$ 5B2 10B1 2A $bc^{21}$
$C_5:D_{70}$ 10C1 $10$ $2$ $C_5\times C_{70}$ 5C1 10C3 2A $b^{4}c^{7}$
$C_5:D_{70}$ 10C3 $10$ $2$ $C_5\times C_{70}$ 5C2 10C1 2A $b^{2}c^{21}$
$C_5:D_{70}$ 10D1 $10$ $2$ $C_5\times C_{70}$ 5D1 10D3 2A $bc^{7}$
$C_5:D_{70}$ 10D3 $10$ $2$ $C_5\times C_{70}$ 5D2 10D1 2A $b^{3}c^{21}$
$C_5:D_{70}$ 10E1 $10$ $2$ $C_5\times C_{70}$ 5E1 10E3 2A $b^{3}c^{7}$
$C_5:D_{70}$ 10E3 $10$ $2$ $C_5\times C_{70}$ 5E2 10E1 2A $b^{4}c^{21}$
$C_5:D_{70}$ 10F1 $10$ $2$ $C_5\times C_{70}$ 5F1 10F3 2A $b^{2}c^{35}$
$C_5:D_{70}$ 10F3 $10$ $2$ $C_5\times C_{70}$ 5F2 10F1 2A $bc^{35}$
$C_5:D_{70}$ 14A1 $14$ $2$ $C_5\times C_{70}$ 7A1 14A3 14A5 $c^{5}$
$C_5:D_{70}$ 14A3 $14$ $2$ $C_5\times C_{70}$ 7A3 14A5 14A1 $c^{15}$
$C_5:D_{70}$ 14A5 $14$ $2$ $C_5\times C_{70}$ 7A2 14A1 14A3 $c^{25}$
$C_5:D_{70}$ 35A1 $35$ $2$ $C_5\times C_{70}$ 35A2 35A3 7A1 $c^{2}$
$C_5:D_{70}$ 35A2 $35$ $2$ $C_5\times C_{70}$ 35A4 35A6 7A2 $c^{4}$
$C_5:D_{70}$ 35A3 $35$ $2$ $C_5\times C_{70}$ 35A6 35A9 7A3 $c^{6}$
$C_5:D_{70}$ 35A4 $35$ $2$ $C_5\times C_{70}$ 35A8 35A12 7A3 $c^{8}$
$C_5:D_{70}$ 35A6 $35$ $2$ $C_5\times C_{70}$ 35A12 35A17 7A1 $c^{12}$
$C_5:D_{70}$ 35A8 $35$ $2$ $C_5\times C_{70}$ 35A16 35A11 7A1 $c^{16}$
$C_5:D_{70}$ 35A9 $35$ $2$ $C_5\times C_{70}$ 35A17 35A8 7A2 $c^{18}$
$C_5:D_{70}$ 35A11 $35$ $2$ $C_5\times C_{70}$ 35A13 35A2 7A3 $c^{22}$
$C_5:D_{70}$ 35A12 $35$ $2$ $C_5\times C_{70}$ 35A11 35A1 7A2 $c^{24}$
$C_5:D_{70}$ 35A13 $35$ $2$ $C_5\times C_{70}$ 35A9 35A4 7A1 $c^{26}$
$C_5:D_{70}$ 35A16 $35$ $2$ $C_5\times C_{70}$ 35A3 35A13 7A2 $c^{32}$
$C_5:D_{70}$ 35A17 $35$ $2$ $C_5\times C_{70}$ 35A1 35A16 7A3 $c^{34}$
$C_5:D_{70}$ 35B1 $35$ $2$ $C_5\times C_{70}$ 35B2 35B3 7A1 $b^{2}c^{2}$
$C_5:D_{70}$ 35B2 $35$ $2$ $C_5\times C_{70}$ 35B4 35B6 7A2 $b^{4}c^{4}$
$C_5:D_{70}$ 35B3 $35$ $2$ $C_5\times C_{70}$ 35B6 35B9 7A3 $bc^{6}$
$C_5:D_{70}$ 35B4 $35$ $2$ $C_5\times C_{70}$ 35B8 35B12 7A3 $b^{3}c^{8}$
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