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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b, c, d \mid a^{2}=b^{2}=c^{2}=d^{204}=1 \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 17P
$C_2^3\times C_{204}$ 1A $1$ $1$ $C_2^3\times C_{204}$ 1A 1A 1A $1$
$C_2^3\times C_{204}$ 2A $2$ $1$ $C_2^3\times C_{204}$ 1A 2A 2A $c$
$C_2^3\times C_{204}$ 2B $2$ $1$ $C_2^3\times C_{204}$ 1A 2B 2B $cd^{102}$
$C_2^3\times C_{204}$ 2C $2$ $1$ $C_2^3\times C_{204}$ 1A 2C 2C $b$
$C_2^3\times C_{204}$ 2D $2$ $1$ $C_2^3\times C_{204}$ 1A 2D 2D $bd^{102}$
$C_2^3\times C_{204}$ 2E $2$ $1$ $C_2^3\times C_{204}$ 1A 2E 2E $a$
$C_2^3\times C_{204}$ 2F $2$ $1$ $C_2^3\times C_{204}$ 1A 2F 2F $ad^{102}$
$C_2^3\times C_{204}$ 2G $2$ $1$ $C_2^3\times C_{204}$ 1A 2G 2G $bc$
$C_2^3\times C_{204}$ 2H $2$ $1$ $C_2^3\times C_{204}$ 1A 2H 2H $bcd^{102}$
$C_2^3\times C_{204}$ 2I $2$ $1$ $C_2^3\times C_{204}$ 1A 2I 2I $ac$
$C_2^3\times C_{204}$ 2J $2$ $1$ $C_2^3\times C_{204}$ 1A 2J 2J $acd^{102}$
$C_2^3\times C_{204}$ 2K $2$ $1$ $C_2^3\times C_{204}$ 1A 2K 2K $ab$
$C_2^3\times C_{204}$ 2L $2$ $1$ $C_2^3\times C_{204}$ 1A 2L 2L $abd^{102}$
$C_2^3\times C_{204}$ 2M $2$ $1$ $C_2^3\times C_{204}$ 1A 2M 2M $abc$
$C_2^3\times C_{204}$ 2N $2$ $1$ $C_2^3\times C_{204}$ 1A 2N 2N $abcd^{102}$
$C_2^3\times C_{204}$ 2O $2$ $1$ $C_2^3\times C_{204}$ 1A 2O 2O $d^{102}$
$C_2^3\times C_{204}$ 3A1 $3$ $1$ $C_2^3\times C_{204}$ 3A-1 1A 3A-1 $d^{136}$
$C_2^3\times C_{204}$ 3A-1 $3$ $1$ $C_2^3\times C_{204}$ 3A1 1A 3A1 $d^{68}$
$C_2^3\times C_{204}$ 4A1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4A-1 4A1 $d^{51}$
$C_2^3\times C_{204}$ 4A-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4A1 4A-1 $d^{153}$
$C_2^3\times C_{204}$ 4B1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4B-1 4B1 $cd^{51}$
$C_2^3\times C_{204}$ 4B-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4B1 4B-1 $cd^{153}$
$C_2^3\times C_{204}$ 4C1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4C-1 4C1 $bd^{51}$
$C_2^3\times C_{204}$ 4C-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4C1 4C-1 $bd^{153}$
$C_2^3\times C_{204}$ 4D1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4D-1 4D1 $ad^{51}$
$C_2^3\times C_{204}$ 4D-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4D1 4D-1 $ad^{153}$
$C_2^3\times C_{204}$ 4E1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4E-1 4E1 $bcd^{51}$
$C_2^3\times C_{204}$ 4E-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4E1 4E-1 $bcd^{153}$
$C_2^3\times C_{204}$ 4F1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4F-1 4F1 $acd^{51}$
$C_2^3\times C_{204}$ 4F-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4F1 4F-1 $acd^{153}$
$C_2^3\times C_{204}$ 4G1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4G-1 4G1 $abd^{51}$
$C_2^3\times C_{204}$ 4G-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4G1 4G-1 $abd^{153}$
$C_2^3\times C_{204}$ 4H1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4H-1 4H1 $abcd^{51}$
$C_2^3\times C_{204}$ 4H-1 $4$ $1$ $C_2^3\times C_{204}$ 2O 4H1 4H-1 $abcd^{153}$
$C_2^3\times C_{204}$ 6A1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2A 6A-1 $cd^{68}$
$C_2^3\times C_{204}$ 6A-1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2A 6A1 $cd^{136}$
$C_2^3\times C_{204}$ 6B1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2B 6B-1 $cd^{34}$
$C_2^3\times C_{204}$ 6B-1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2B 6B1 $cd^{170}$
$C_2^3\times C_{204}$ 6C1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2C 6C-1 $bd^{68}$
$C_2^3\times C_{204}$ 6C-1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2C 6C1 $bd^{136}$
$C_2^3\times C_{204}$ 6D1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2D 6D-1 $bd^{34}$
$C_2^3\times C_{204}$ 6D-1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2D 6D1 $bd^{170}$
$C_2^3\times C_{204}$ 6E1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2E 6E-1 $ad^{68}$
$C_2^3\times C_{204}$ 6E-1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2E 6E1 $ad^{136}$
$C_2^3\times C_{204}$ 6F1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2F 6F-1 $ad^{34}$
$C_2^3\times C_{204}$ 6F-1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2F 6F1 $ad^{170}$
$C_2^3\times C_{204}$ 6G1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2G 6G-1 $bcd^{68}$
$C_2^3\times C_{204}$ 6G-1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2G 6G1 $bcd^{136}$
$C_2^3\times C_{204}$ 6H1 $6$ $1$ $C_2^3\times C_{204}$ 3A-1 2H 6H-1 $bcd^{34}$
$C_2^3\times C_{204}$ 6H-1 $6$ $1$ $C_2^3\times C_{204}$ 3A1 2H 6H1 $bcd^{170}$
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