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Results (24 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{42}=1, b^{a}=b^{41} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 3P 7P
$D_{42}$ 1A $1$ $1$ $D_{42}$ 1A 1A 1A $1$
$D_{42}$ 2A $2$ $1$ $D_{42}$ 1A 2A 2A $b^{21}$
$D_{42}$ 2B $2$ $21$ $C_2^2$ 1A 2B 2B $ab^{36}$
$D_{42}$ 2C $2$ $21$ $C_2^2$ 1A 2C 2C $ab^{5}$
$D_{42}$ 3A $3$ $2$ $C_{42}$ 3A 1A 3A $b^{14}$
$D_{42}$ 6A $6$ $2$ $C_{42}$ 3A 2A 6A $b^{7}$
$D_{42}$ 7A1 $7$ $2$ $C_{42}$ 7A2 7A3 1A $b^{6}$
$D_{42}$ 7A2 $7$ $2$ $C_{42}$ 7A3 7A1 1A $b^{12}$
$D_{42}$ 7A3 $7$ $2$ $C_{42}$ 7A1 7A2 1A $b^{18}$
$D_{42}$ 14A1 $14$ $2$ $C_{42}$ 7A1 14A3 2A $b^{3}$
$D_{42}$ 14A3 $14$ $2$ $C_{42}$ 7A3 14A5 2A $b^{9}$
$D_{42}$ 14A5 $14$ $2$ $C_{42}$ 7A2 14A1 2A $b^{15}$
$D_{42}$ 21A1 $21$ $2$ $C_{42}$ 21A2 7A1 3A $b^{2}$
$D_{42}$ 21A2 $21$ $2$ $C_{42}$ 21A4 7A2 3A $b^{4}$
$D_{42}$ 21A4 $21$ $2$ $C_{42}$ 21A8 7A3 3A $b^{8}$
$D_{42}$ 21A5 $21$ $2$ $C_{42}$ 21A10 7A2 3A $b^{10}$
$D_{42}$ 21A8 $21$ $2$ $C_{42}$ 21A5 7A1 3A $b^{16}$
$D_{42}$ 21A10 $21$ $2$ $C_{42}$ 21A1 7A3 3A $b^{20}$
$D_{42}$ 42A1 $42$ $2$ $C_{42}$ 21A1 14A1 6A $b$
$D_{42}$ 42A5 $42$ $2$ $C_{42}$ 21A5 14A5 6A $b^{5}$
$D_{42}$ 42A11 $42$ $2$ $C_{42}$ 21A10 14A3 6A $b^{31}$
$D_{42}$ 42A13 $42$ $2$ $C_{42}$ 21A8 14A1 6A $b^{13}$
$D_{42}$ 42A17 $42$ $2$ $C_{42}$ 21A4 14A3 6A $b^{25}$
$D_{42}$ 42A19 $42$ $2$ $C_{42}$ 21A2 14A5 6A $b^{19}$
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