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Results (36 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{66}=1, b^{a}=b^{65} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 11P
$D_{66}$ 1A $1$ $1$ $D_{66}$ 1A 1A 1A $1$
$D_{66}$ 2A $2$ $1$ $D_{66}$ 1A 2A 2A $b^{33}$
$D_{66}$ 2B $2$ $33$ $C_2^2$ 1A 2B 2B $ab^{60}$
$D_{66}$ 2C $2$ $33$ $C_2^2$ 1A 2C 2C $ab^{5}$
$D_{66}$ 3A $3$ $2$ $C_{66}$ 3A 1A 3A $b^{22}$
$D_{66}$ 6A $6$ $2$ $C_{66}$ 3A 2A 6A $b^{11}$
$D_{66}$ 11A1 $11$ $2$ $C_{66}$ 11A2 11A3 11A5 $b^{6}$
$D_{66}$ 11A2 $11$ $2$ $C_{66}$ 11A4 11A5 11A1 $b^{12}$
$D_{66}$ 11A3 $11$ $2$ $C_{66}$ 11A5 11A2 11A4 $b^{18}$
$D_{66}$ 11A4 $11$ $2$ $C_{66}$ 11A3 11A1 11A2 $b^{24}$
$D_{66}$ 11A5 $11$ $2$ $C_{66}$ 11A1 11A4 11A3 $b^{30}$
$D_{66}$ 22A1 $22$ $2$ $C_{66}$ 11A1 22A3 22A5 $b^{3}$
$D_{66}$ 22A3 $22$ $2$ $C_{66}$ 11A3 22A9 22A7 $b^{9}$
$D_{66}$ 22A5 $22$ $2$ $C_{66}$ 11A5 22A7 22A3 $b^{15}$
$D_{66}$ 22A7 $22$ $2$ $C_{66}$ 11A4 22A1 22A9 $b^{21}$
$D_{66}$ 22A9 $22$ $2$ $C_{66}$ 11A2 22A5 22A1 $b^{27}$
$D_{66}$ 33A1 $33$ $2$ $C_{66}$ 33A2 11A1 33A5 $b^{2}$
$D_{66}$ 33A2 $33$ $2$ $C_{66}$ 33A4 11A2 33A10 $b^{4}$
$D_{66}$ 33A4 $33$ $2$ $C_{66}$ 33A8 11A4 33A13 $b^{8}$
$D_{66}$ 33A5 $33$ $2$ $C_{66}$ 33A10 11A5 33A8 $b^{10}$
$D_{66}$ 33A7 $33$ $2$ $C_{66}$ 33A14 11A4 33A2 $b^{14}$
$D_{66}$ 33A8 $33$ $2$ $C_{66}$ 33A16 11A3 33A7 $b^{16}$
$D_{66}$ 33A10 $33$ $2$ $C_{66}$ 33A13 11A1 33A16 $b^{20}$
$D_{66}$ 33A13 $33$ $2$ $C_{66}$ 33A7 11A2 33A1 $b^{26}$
$D_{66}$ 33A14 $33$ $2$ $C_{66}$ 33A5 11A3 33A4 $b^{28}$
$D_{66}$ 33A16 $33$ $2$ $C_{66}$ 33A1 11A5 33A14 $b^{32}$
$D_{66}$ 66A1 $66$ $2$ $C_{66}$ 33A1 22A1 66A5 $b$
$D_{66}$ 66A5 $66$ $2$ $C_{66}$ 33A5 22A5 66A25 $b^{5}$
$D_{66}$ 66A7 $66$ $2$ $C_{66}$ 33A7 22A7 66A31 $b^{7}$
$D_{66}$ 66A13 $66$ $2$ $C_{66}$ 33A13 22A9 66A1 $b^{13}$
$D_{66}$ 66A17 $66$ $2$ $C_{66}$ 33A16 22A5 66A19 $b^{49}$
$D_{66}$ 66A19 $66$ $2$ $C_{66}$ 33A14 22A3 66A29 $b^{19}$
$D_{66}$ 66A23 $66$ $2$ $C_{66}$ 33A10 22A1 66A17 $b^{43}$
$D_{66}$ 66A25 $66$ $2$ $C_{66}$ 33A8 22A3 66A7 $b^{25}$
$D_{66}$ 66A29 $66$ $2$ $C_{66}$ 33A4 22A7 66A13 $b^{37}$
$D_{66}$ 66A31 $66$ $2$ $C_{66}$ 33A2 22A9 66A23 $b^{31}$
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