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Results (19 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{18}=b^{19}=1, b^{a}=b^{2} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 19P
$F_{19}$ 1A $1$ $1$ $F_{19}$ 1A 1A 1A $1$
$F_{19}$ 2A $2$ $19$ $C_{18}$ 1A 2A 2A $a^{9}b^{11}$
$F_{19}$ 3A1 $3$ $19$ $C_{18}$ 3A-1 1A 3A1 $a^{12}b^{2}$
$F_{19}$ 3A-1 $3$ $19$ $C_{18}$ 3A1 1A 3A-1 $a^{6}b^{5}$
$F_{19}$ 6A1 $6$ $19$ $C_{18}$ 3A1 2A 6A1 $a^{15}b^{6}$
$F_{19}$ 6A-1 $6$ $19$ $C_{18}$ 3A-1 2A 6A-1 $a^{3}b^{9}$
$F_{19}$ 9A1 $9$ $19$ $C_{18}$ 9A2 3A1 9A1 $a^{10}b^{7}$
$F_{19}$ 9A-1 $9$ $19$ $C_{18}$ 9A-2 3A-1 9A-1 $a^{8}b^{13}$
$F_{19}$ 9A2 $9$ $19$ $C_{18}$ 9A4 3A-1 9A2 $a^{2}b^{12}$
$F_{19}$ 9A-2 $9$ $19$ $C_{18}$ 9A-4 3A1 9A-2 $a^{16}b^{16}$
$F_{19}$ 9A4 $9$ $19$ $C_{18}$ 9A-1 3A1 9A4 $a^{4}b^{3}$
$F_{19}$ 9A-4 $9$ $19$ $C_{18}$ 9A1 3A-1 9A-4 $a^{14}b$
$F_{19}$ 18A1 $18$ $19$ $C_{18}$ 9A1 6A1 18A1 $a^{5}b^{10}$
$F_{19}$ 18A-1 $18$ $19$ $C_{18}$ 9A-1 6A-1 18A-1 $a^{13}b^{8}$
$F_{19}$ 18A5 $18$ $19$ $C_{18}$ 9A-4 6A-1 18A5 $a^{7}b^{14}$
$F_{19}$ 18A-5 $18$ $19$ $C_{18}$ 9A4 6A1 18A-5 $a^{11}b^{18}$
$F_{19}$ 18A7 $18$ $19$ $C_{18}$ 9A-2 6A1 18A7 $a^{17}b^{17}$
$F_{19}$ 18A-7 $18$ $19$ $C_{18}$ 9A2 6A-1 18A-7 $ab^{4}$
$F_{19}$ 19A $19$ $18$ $C_{19}$ 19A 19A 1A $b$
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