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Results (27 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b, c, d \mid a^{26}=b^{3}=c^{3}=d^{3}=[b,c]=[b,d]=[c,d]=1, b^{a}=d^{2}, c^{a}=bd^{2}, d^{a}=b^{2}cd \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 13P
$F_{27}$ 1A $1$ $1$ $F_{27}$ 1A 1A 1A $1$
$F_{27}$ 2A $2$ $27$ $C_{26}$ 1A 2A 2A $a^{13}c^{2}$
$F_{27}$ 3A $3$ $26$ $C_3^3$ 3A 1A 3A $d$
$F_{27}$ 13A1 $13$ $27$ $C_{26}$ 13A2 13A3 1A $a^{24}bd^{2}$
$F_{27}$ 13A-1 $13$ $27$ $C_{26}$ 13A-2 13A-3 1A $a^{2}b^{2}c^{2}d^{2}$
$F_{27}$ 13A2 $13$ $27$ $C_{26}$ 13A4 13A6 1A $a^{22}bc$
$F_{27}$ 13A-2 $13$ $27$ $C_{26}$ 13A-4 13A-6 1A $a^{4}d$
$F_{27}$ 13A3 $13$ $27$ $C_{26}$ 13A6 13A-4 1A $a^{20}bcd$
$F_{27}$ 13A-3 $13$ $27$ $C_{26}$ 13A-6 13A4 1A $a^{6}b^{2}$
$F_{27}$ 13A4 $13$ $27$ $C_{26}$ 13A-5 13A-1 1A $a^{18}b^{2}d$
$F_{27}$ 13A-4 $13$ $27$ $C_{26}$ 13A5 13A1 1A $a^{8}b$
$F_{27}$ 13A5 $13$ $27$ $C_{26}$ 13A-3 13A2 1A $a^{16}bc^{2}d$
$F_{27}$ 13A-5 $13$ $27$ $C_{26}$ 13A3 13A-2 1A $a^{10}cd$
$F_{27}$ 13A6 $13$ $27$ $C_{26}$ 13A-1 13A5 1A $a^{14}bcd^{2}$
$F_{27}$ 13A-6 $13$ $27$ $C_{26}$ 13A1 13A-5 1A $a^{12}c^{2}d$
$F_{27}$ 26A1 $26$ $27$ $C_{26}$ 13A1 26A3 2A $a^{25}d^{2}$
$F_{27}$ 26A-1 $26$ $27$ $C_{26}$ 13A-1 26A-3 2A $ab^{2}cd$
$F_{27}$ 26A3 $26$ $27$ $C_{26}$ 13A3 26A9 2A $a^{23}cd^{2}$
$F_{27}$ 26A-3 $26$ $27$ $C_{26}$ 13A-3 26A-9 2A $a^{3}b^{2}d^{2}$
$F_{27}$ 26A5 $26$ $27$ $C_{26}$ 13A5 26A-11 2A $a^{21}b^{2}c^{2}$
$F_{27}$ 26A-5 $26$ $27$ $C_{26}$ 13A-5 26A11 2A $a^{5}bc^{2}d^{2}$
$F_{27}$ 26A7 $26$ $27$ $C_{26}$ 13A-6 26A-5 2A $a^{19}bc^{2}$
$F_{27}$ 26A-7 $26$ $27$ $C_{26}$ 13A6 26A5 2A $a^{7}b^{2}cd^{2}$
$F_{27}$ 26A9 $26$ $27$ $C_{26}$ 13A-4 26A1 2A $a^{17}c^{2}d^{2}$
$F_{27}$ 26A-9 $26$ $27$ $C_{26}$ 13A4 26A-1 2A $a^{9}b^{2}c$
$F_{27}$ 26A11 $26$ $27$ $C_{26}$ 13A-2 26A7 2A $a^{15}bd$
$F_{27}$ 26A-11 $26$ $27$ $C_{26}$ 13A2 26A-7 2A $a^{11}b^{2}c^{2}d$
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