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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{4}=c^{166}=[a,c]=[b,c]=1, b^{a}=bc^{83} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 83P
$C_2^2:C_{332}$ 1A $1$ $1$ $C_2^2:C_{332}$ 1A 1A $1$
$C_2^2:C_{332}$ 2A $2$ $1$ $C_2^2:C_{332}$ 1A 2A $c^{83}$
$C_2^2:C_{332}$ 2B $2$ $1$ $C_2^2:C_{332}$ 1A 2B $b^{2}$
$C_2^2:C_{332}$ 2C $2$ $1$ $C_2^2:C_{332}$ 1A 2C $b^{2}c^{83}$
$C_2^2:C_{332}$ 2D $2$ $2$ $C_2^2\times C_{166}$ 1A 2D $a$
$C_2^2:C_{332}$ 2E $2$ $2$ $C_2^2\times C_{166}$ 1A 2E $ab^{2}$
$C_2^2:C_{332}$ 4A1 $4$ $2$ $C_2\times C_{332}$ 2B 4A1 $b^{3}$
$C_2^2:C_{332}$ 4A-1 $4$ $2$ $C_2\times C_{332}$ 2B 4A-1 $b$
$C_2^2:C_{332}$ 4B1 $4$ $2$ $C_2\times C_{332}$ 2C 4B1 $ab^{3}c^{83}$
$C_2^2:C_{332}$ 4B-1 $4$ $2$ $C_2\times C_{332}$ 2C 4B-1 $ab$
$C_2^2:C_{332}$ 83A1 $83$ $1$ $C_2^2:C_{332}$ 83A2 83A41 $c^{2}$
$C_2^2:C_{332}$ 83A-1 $83$ $1$ $C_2^2:C_{332}$ 83A-2 83A-41 $c^{164}$
$C_2^2:C_{332}$ 83A2 $83$ $1$ $C_2^2:C_{332}$ 83A4 83A-1 $c^{4}$
$C_2^2:C_{332}$ 83A-2 $83$ $1$ $C_2^2:C_{332}$ 83A-4 83A1 $c^{162}$
$C_2^2:C_{332}$ 83A3 $83$ $1$ $C_2^2:C_{332}$ 83A6 83A40 $c^{6}$
$C_2^2:C_{332}$ 83A-3 $83$ $1$ $C_2^2:C_{332}$ 83A-6 83A-40 $c^{160}$
$C_2^2:C_{332}$ 83A4 $83$ $1$ $C_2^2:C_{332}$ 83A8 83A-2 $c^{8}$
$C_2^2:C_{332}$ 83A-4 $83$ $1$ $C_2^2:C_{332}$ 83A-8 83A2 $c^{158}$
$C_2^2:C_{332}$ 83A5 $83$ $1$ $C_2^2:C_{332}$ 83A10 83A39 $c^{10}$
$C_2^2:C_{332}$ 83A-5 $83$ $1$ $C_2^2:C_{332}$ 83A-10 83A-39 $c^{156}$
$C_2^2:C_{332}$ 83A6 $83$ $1$ $C_2^2:C_{332}$ 83A12 83A-3 $c^{12}$
$C_2^2:C_{332}$ 83A-6 $83$ $1$ $C_2^2:C_{332}$ 83A-12 83A3 $c^{154}$
$C_2^2:C_{332}$ 83A7 $83$ $1$ $C_2^2:C_{332}$ 83A14 83A38 $c^{14}$
$C_2^2:C_{332}$ 83A-7 $83$ $1$ $C_2^2:C_{332}$ 83A-14 83A-38 $c^{152}$
$C_2^2:C_{332}$ 83A8 $83$ $1$ $C_2^2:C_{332}$ 83A16 83A-4 $c^{16}$
$C_2^2:C_{332}$ 83A-8 $83$ $1$ $C_2^2:C_{332}$ 83A-16 83A4 $c^{150}$
$C_2^2:C_{332}$ 83A9 $83$ $1$ $C_2^2:C_{332}$ 83A18 83A37 $c^{18}$
$C_2^2:C_{332}$ 83A-9 $83$ $1$ $C_2^2:C_{332}$ 83A-18 83A-37 $c^{148}$
$C_2^2:C_{332}$ 83A10 $83$ $1$ $C_2^2:C_{332}$ 83A20 83A-5 $c^{20}$
$C_2^2:C_{332}$ 83A-10 $83$ $1$ $C_2^2:C_{332}$ 83A-20 83A5 $c^{146}$
$C_2^2:C_{332}$ 83A11 $83$ $1$ $C_2^2:C_{332}$ 83A22 83A36 $c^{22}$
$C_2^2:C_{332}$ 83A-11 $83$ $1$ $C_2^2:C_{332}$ 83A-22 83A-36 $c^{144}$
$C_2^2:C_{332}$ 83A12 $83$ $1$ $C_2^2:C_{332}$ 83A24 83A-6 $c^{24}$
$C_2^2:C_{332}$ 83A-12 $83$ $1$ $C_2^2:C_{332}$ 83A-24 83A6 $c^{142}$
$C_2^2:C_{332}$ 83A13 $83$ $1$ $C_2^2:C_{332}$ 83A26 83A35 $c^{26}$
$C_2^2:C_{332}$ 83A-13 $83$ $1$ $C_2^2:C_{332}$ 83A-26 83A-35 $c^{140}$
$C_2^2:C_{332}$ 83A14 $83$ $1$ $C_2^2:C_{332}$ 83A28 83A-7 $c^{28}$
$C_2^2:C_{332}$ 83A-14 $83$ $1$ $C_2^2:C_{332}$ 83A-28 83A7 $c^{138}$
$C_2^2:C_{332}$ 83A15 $83$ $1$ $C_2^2:C_{332}$ 83A30 83A34 $c^{30}$
$C_2^2:C_{332}$ 83A-15 $83$ $1$ $C_2^2:C_{332}$ 83A-30 83A-34 $c^{136}$
$C_2^2:C_{332}$ 83A16 $83$ $1$ $C_2^2:C_{332}$ 83A32 83A-8 $c^{32}$
$C_2^2:C_{332}$ 83A-16 $83$ $1$ $C_2^2:C_{332}$ 83A-32 83A8 $c^{134}$
$C_2^2:C_{332}$ 83A17 $83$ $1$ $C_2^2:C_{332}$ 83A34 83A33 $c^{34}$
$C_2^2:C_{332}$ 83A-17 $83$ $1$ $C_2^2:C_{332}$ 83A-34 83A-33 $c^{132}$
$C_2^2:C_{332}$ 83A18 $83$ $1$ $C_2^2:C_{332}$ 83A36 83A-9 $c^{36}$
$C_2^2:C_{332}$ 83A-18 $83$ $1$ $C_2^2:C_{332}$ 83A-36 83A9 $c^{130}$
$C_2^2:C_{332}$ 83A19 $83$ $1$ $C_2^2:C_{332}$ 83A38 83A32 $c^{38}$
$C_2^2:C_{332}$ 83A-19 $83$ $1$ $C_2^2:C_{332}$ 83A-38 83A-32 $c^{128}$
$C_2^2:C_{332}$ 83A20 $83$ $1$ $C_2^2:C_{332}$ 83A40 83A-10 $c^{40}$
$C_2^2:C_{332}$ 83A-20 $83$ $1$ $C_2^2:C_{332}$ 83A-40 83A10 $c^{126}$
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