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Results (32 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{6}=b^{5}=c^{5}=d^{5}=[b,c]=[b,d]=[c,d]=1, b^{a}=b^{4}, c^{a}=d^{3}, d^{a}=c^{3}d \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_5^3:C_6$ 1A $1$ $1$ $C_5^3:C_6$ 1A 1A 1A $1$
$C_5^3:C_6$ 2A $2$ $125$ $C_6$ 1A 2A 2A $a^{3}c^{2}d^{2}$
$C_5^3:C_6$ 3A1 $3$ $25$ $C_3\times D_5$ 3A-1 1A 3A-1 $a^{4}$
$C_5^3:C_6$ 3A-1 $3$ $25$ $C_3\times D_5$ 3A1 1A 3A1 $a^{2}$
$C_5^3:C_6$ 5A1 $5$ $2$ $C_5\wr C_3$ 5A2 5A2 1A $b^{3}$
$C_5^3:C_6$ 5A2 $5$ $2$ $C_5\wr C_3$ 5A1 5A1 1A $b$
$C_5^3:C_6$ 5B1 $5$ $6$ $C_5^3$ 5B2 5B2 1A $d$
$C_5^3:C_6$ 5B2 $5$ $6$ $C_5^3$ 5B1 5B1 1A $c$
$C_5^3:C_6$ 5C1 $5$ $6$ $C_5^3$ 5C2 5C2 1A $cd$
$C_5^3:C_6$ 5C2 $5$ $6$ $C_5^3$ 5C1 5C1 1A $cd^{3}$
$C_5^3:C_6$ 5D1 $5$ $6$ $C_5^3$ 5D2 5D2 1A $bd$
$C_5^3:C_6$ 5D2 $5$ $6$ $C_5^3$ 5D1 5D1 1A $b^{2}c$
$C_5^3:C_6$ 5E1 $5$ $6$ $C_5^3$ 5E2 5E2 1A $bc$
$C_5^3:C_6$ 5E2 $5$ $6$ $C_5^3$ 5E1 5E1 1A $b^{2}c^{2}$
$C_5^3:C_6$ 5F1 $5$ $6$ $C_5^3$ 5F2 5F2 1A $bc^{2}$
$C_5^3:C_6$ 5F2 $5$ $6$ $C_5^3$ 5F1 5F1 1A $b^{3}c$
$C_5^3:C_6$ 5G1 $5$ $6$ $C_5^3$ 5G2 5G2 1A $b^{2}d$
$C_5^3:C_6$ 5G2 $5$ $6$ $C_5^3$ 5G1 5G1 1A $bd^{3}$
$C_5^3:C_6$ 5H1 $5$ $6$ $C_5^3$ 5H2 5H2 1A $bcd$
$C_5^3:C_6$ 5H2 $5$ $6$ $C_5^3$ 5H1 5H1 1A $b^{2}c^{2}d^{2}$
$C_5^3:C_6$ 5I1 $5$ $6$ $C_5^3$ 5I2 5I2 1A $b^{2}cd$
$C_5^3:C_6$ 5I2 $5$ $6$ $C_5^3$ 5I1 5I1 1A $bcd^{3}$
$C_5^3:C_6$ 5J1 $5$ $6$ $C_5^3$ 5J2 5J2 1A $bc^{2}d^{2}$
$C_5^3:C_6$ 5J2 $5$ $6$ $C_5^3$ 5J1 5J1 1A $b^{3}cd$
$C_5^3:C_6$ 5K1 $5$ $6$ $C_5^3$ 5K2 5K2 1A $bc^{3}d^{2}$
$C_5^3:C_6$ 5K2 $5$ $6$ $C_5^3$ 5K1 5K1 1A $b^{2}cd^{3}$
$C_5^3:C_6$ 6A1 $6$ $125$ $C_6$ 3A-1 2A 6A-1 $ac^{3}d^{2}$
$C_5^3:C_6$ 6A-1 $6$ $125$ $C_6$ 3A1 2A 6A1 $a^{5}c^{3}d^{4}$
$C_5^3:C_6$ 15A1 $15$ $50$ $C_{15}$ 15A2 5A1 3A1 $a^{2}b$
$C_5^3:C_6$ 15A-1 $15$ $50$ $C_{15}$ 15A-2 5A1 3A-1 $a^{4}b^{4}$
$C_5^3:C_6$ 15A2 $15$ $50$ $C_{15}$ 15A1 5A2 3A-1 $a^{4}b^{2}$
$C_5^3:C_6$ 15A-2 $15$ $50$ $C_{15}$ 15A-1 5A2 3A1 $a^{2}b^{3}$
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