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Results (48 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{3}=c^{15}=[b,c]=1, b^{a}=b^{2}, c^{a}=c^{14} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$C_6.D_{15}$ 1A $1$ $1$ $C_6.D_{15}$ 1A 1A 1A $1$
$C_6.D_{15}$ 2A $2$ $1$ $C_6.D_{15}$ 1A 2A 2A $a^{2}$
$C_6.D_{15}$ 3A $3$ $2$ $C_3\times C_{30}$ 3A 1A 3A $c^{10}$
$C_6.D_{15}$ 3B $3$ $2$ $C_3\times C_{30}$ 3B 1A 3B $b$
$C_6.D_{15}$ 3C $3$ $2$ $C_3\times C_{30}$ 3C 1A 3C $bc^{10}$
$C_6.D_{15}$ 3D $3$ $2$ $C_3\times C_{30}$ 3D 1A 3D $bc^{5}$
$C_6.D_{15}$ 4A1 $4$ $45$ $C_4$ 2A 4A-1 4A1 $ac^{11}$
$C_6.D_{15}$ 4A-1 $4$ $45$ $C_4$ 2A 4A1 4A-1 $a^{3}c^{11}$
$C_6.D_{15}$ 5A1 $5$ $2$ $C_3\times C_{30}$ 5A2 5A2 1A $c^{6}$
$C_6.D_{15}$ 5A2 $5$ $2$ $C_3\times C_{30}$ 5A1 5A1 1A $c^{12}$
$C_6.D_{15}$ 6A $6$ $2$ $C_3\times C_{30}$ 3A 2A 6A $a^{2}c^{5}$
$C_6.D_{15}$ 6B $6$ $2$ $C_3\times C_{30}$ 3B 2A 6B $a^{2}b^{2}$
$C_6.D_{15}$ 6C $6$ $2$ $C_3\times C_{30}$ 3C 2A 6C $a^{2}b^{2}c^{5}$
$C_6.D_{15}$ 6D $6$ $2$ $C_3\times C_{30}$ 3D 2A 6D $a^{2}b^{2}c^{10}$
$C_6.D_{15}$ 10A1 $10$ $2$ $C_3\times C_{30}$ 5A1 10A3 2A $a^{2}c^{3}$
$C_6.D_{15}$ 10A3 $10$ $2$ $C_3\times C_{30}$ 5A2 10A1 2A $a^{2}c^{9}$
$C_6.D_{15}$ 15A1 $15$ $2$ $C_3\times C_{30}$ 15A2 5A1 3A $c^{2}$
$C_6.D_{15}$ 15A2 $15$ $2$ $C_3\times C_{30}$ 15A4 5A2 3A $c^{4}$
$C_6.D_{15}$ 15A4 $15$ $2$ $C_3\times C_{30}$ 15A7 5A1 3A $c^{8}$
$C_6.D_{15}$ 15A7 $15$ $2$ $C_3\times C_{30}$ 15A1 5A2 3A $c^{14}$
$C_6.D_{15}$ 15B1 $15$ $2$ $C_3\times C_{30}$ 15B2 5A2 3B $b^{2}c^{6}$
$C_6.D_{15}$ 15B2 $15$ $2$ $C_3\times C_{30}$ 15B4 5A1 3B $bc^{12}$
$C_6.D_{15}$ 15B4 $15$ $2$ $C_3\times C_{30}$ 15B7 5A2 3B $b^{2}c^{9}$
$C_6.D_{15}$ 15B7 $15$ $2$ $C_3\times C_{30}$ 15B1 5A1 3B $b^{2}c^{12}$
$C_6.D_{15}$ 15C1 $15$ $2$ $C_3\times C_{30}$ 15C2 5A1 3C $b^{2}c^{2}$
$C_6.D_{15}$ 15C2 $15$ $2$ $C_3\times C_{30}$ 15C4 5A2 3C $bc^{4}$
$C_6.D_{15}$ 15C4 $15$ $2$ $C_3\times C_{30}$ 15C7 5A1 3C $b^{2}c^{8}$
$C_6.D_{15}$ 15C7 $15$ $2$ $C_3\times C_{30}$ 15C1 5A2 3C $b^{2}c^{14}$
$C_6.D_{15}$ 15D1 $15$ $2$ $C_3\times C_{30}$ 15D2 5A2 3D $b^{2}c^{4}$
$C_6.D_{15}$ 15D2 $15$ $2$ $C_3\times C_{30}$ 15D4 5A1 3D $bc^{8}$
$C_6.D_{15}$ 15D4 $15$ $2$ $C_3\times C_{30}$ 15D7 5A2 3D $b^{2}c$
$C_6.D_{15}$ 15D7 $15$ $2$ $C_3\times C_{30}$ 15D1 5A1 3D $b^{2}c^{13}$
$C_6.D_{15}$ 30A1 $30$ $2$ $C_3\times C_{30}$ 15A1 10A1 6A $a^{2}c$
$C_6.D_{15}$ 30A7 $30$ $2$ $C_3\times C_{30}$ 15A7 10A3 6A $a^{2}c^{7}$
$C_6.D_{15}$ 30A11 $30$ $2$ $C_3\times C_{30}$ 15A4 10A1 6A $a^{2}c^{4}$
$C_6.D_{15}$ 30A13 $30$ $2$ $C_3\times C_{30}$ 15A2 10A3 6A $a^{2}c^{2}$
$C_6.D_{15}$ 30B1 $30$ $2$ $C_3\times C_{30}$ 15B1 10A3 6B $a^{2}bc^{3}$
$C_6.D_{15}$ 30B7 $30$ $2$ $C_3\times C_{30}$ 15B7 10A1 6B $a^{2}bc^{6}$
$C_6.D_{15}$ 30B11 $30$ $2$ $C_3\times C_{30}$ 15B4 10A3 6B $a^{2}b^{2}c^{3}$
$C_6.D_{15}$ 30B13 $30$ $2$ $C_3\times C_{30}$ 15B2 10A1 6B $a^{2}bc^{9}$
$C_6.D_{15}$ 30C1 $30$ $2$ $C_3\times C_{30}$ 15C1 10A1 6C $a^{2}bc$
$C_6.D_{15}$ 30C7 $30$ $2$ $C_3\times C_{30}$ 15C7 10A3 6C $a^{2}bc^{7}$
$C_6.D_{15}$ 30C11 $30$ $2$ $C_3\times C_{30}$ 15C4 10A1 6C $a^{2}bc^{4}$
$C_6.D_{15}$ 30C13 $30$ $2$ $C_3\times C_{30}$ 15C2 10A3 6C $a^{2}b^{2}c^{2}$
$C_6.D_{15}$ 30D1 $30$ $2$ $C_3\times C_{30}$ 15D1 10A3 6D $a^{2}bc^{2}$
$C_6.D_{15}$ 30D7 $30$ $2$ $C_3\times C_{30}$ 15D7 10A1 6D $a^{2}b^{2}c$
$C_6.D_{15}$ 30D11 $30$ $2$ $C_3\times C_{30}$ 15D4 10A3 6D $a^{2}bc^{8}$
$C_6.D_{15}$ 30D13 $30$ $2$ $C_3\times C_{30}$ 15D2 10A1 6D $a^{2}b^{2}c^{4}$
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