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Results (41 matches)

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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{40}=b^{41}=1, b^{a}=b^{22} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 5P 41P
$F_{41}$ 1A $1$ $1$ $F_{41}$ 1A 1A 1A $1$
$F_{41}$ 2A $2$ $41$ $C_{40}$ 1A 2A 2A $a^{20}b^{29}$
$F_{41}$ 4A1 $4$ $41$ $C_{40}$ 2A 4A1 4A1 $a^{30}b^{7}$
$F_{41}$ 4A-1 $4$ $41$ $C_{40}$ 2A 4A-1 4A-1 $a^{10}b^{22}$
$F_{41}$ 5A1 $5$ $41$ $C_{40}$ 5A2 1A 5A1 $a^{32}b^{13}$
$F_{41}$ 5A-1 $5$ $41$ $C_{40}$ 5A-2 1A 5A-1 $a^{8}b^{11}$
$F_{41}$ 5A2 $5$ $41$ $C_{40}$ 5A-1 1A 5A2 $a^{24}b^{20}$
$F_{41}$ 5A-2 $5$ $41$ $C_{40}$ 5A1 1A 5A-2 $a^{16}b^{8}$
$F_{41}$ 8A1 $8$ $41$ $C_{40}$ 4A1 8A-3 8A1 $a^{35}b^{12}$
$F_{41}$ 8A-1 $8$ $41$ $C_{40}$ 4A-1 8A3 8A-1 $a^{5}b^{37}$
$F_{41}$ 8A3 $8$ $41$ $C_{40}$ 4A-1 8A-1 8A3 $a^{25}b^{33}$
$F_{41}$ 8A-3 $8$ $41$ $C_{40}$ 4A1 8A1 8A-3 $a^{15}b^{17}$
$F_{41}$ 10A1 $10$ $41$ $C_{40}$ 5A1 2A 10A1 $a^{36}b^{21}$
$F_{41}$ 10A-1 $10$ $41$ $C_{40}$ 5A-1 2A 10A-1 $a^{4}b^{9}$
$F_{41}$ 10A3 $10$ $41$ $C_{40}$ 5A-2 2A 10A3 $a^{28}b^{18}$
$F_{41}$ 10A-3 $10$ $41$ $C_{40}$ 5A2 2A 10A-3 $a^{12}b^{16}$
$F_{41}$ 20A1 $20$ $41$ $C_{40}$ 10A1 4A1 20A1 $a^{38}b^{24}$
$F_{41}$ 20A-1 $20$ $41$ $C_{40}$ 10A-1 4A-1 20A-1 $a^{2}b^{28}$
$F_{41}$ 20A3 $20$ $41$ $C_{40}$ 10A3 4A-1 20A3 $a^{34}b^{6}$
$F_{41}$ 20A-3 $20$ $41$ $C_{40}$ 10A-3 4A1 20A-3 $a^{6}b^{38}$
$F_{41}$ 20A7 $20$ $41$ $C_{40}$ 10A-3 4A-1 20A7 $a^{26}b^{32}$
$F_{41}$ 20A-7 $20$ $41$ $C_{40}$ 10A3 4A1 20A-7 $a^{14}b^{23}$
$F_{41}$ 20A9 $20$ $41$ $C_{40}$ 10A-1 4A1 20A9 $a^{22}b$
$F_{41}$ 20A-9 $20$ $41$ $C_{40}$ 10A1 4A-1 20A-9 $a^{18}b^{5}$
$F_{41}$ 40A1 $40$ $41$ $C_{40}$ 20A1 8A1 40A1 $a^{39}b^{39}$
$F_{41}$ 40A-1 $40$ $41$ $C_{40}$ 20A-1 8A-1 40A-1 $ab^{3}$
$F_{41}$ 40A3 $40$ $41$ $C_{40}$ 20A3 8A3 40A3 $a^{37}b^{14}$
$F_{41}$ 40A-3 $40$ $41$ $C_{40}$ 20A-3 8A-3 40A-3 $a^{3}b^{4}$
$F_{41}$ 40A7 $40$ $41$ $C_{40}$ 20A7 8A-1 40A7 $a^{33}b^{2}$
$F_{41}$ 40A-7 $40$ $41$ $C_{40}$ 20A-7 8A1 40A-7 $a^{7}b^{19}$
$F_{41}$ 40A9 $40$ $41$ $C_{40}$ 20A9 8A1 40A9 $a^{31}b^{34}$
$F_{41}$ 40A-9 $40$ $41$ $C_{40}$ 20A-9 8A-1 40A-9 $a^{9}b^{40}$
$F_{41}$ 40A11 $40$ $41$ $C_{40}$ 20A-9 8A3 40A11 $a^{29}b^{30}$
$F_{41}$ 40A-11 $40$ $41$ $C_{40}$ 20A9 8A-3 40A-11 $a^{11}b^{36}$
$F_{41}$ 40A13 $40$ $41$ $C_{40}$ 20A-7 8A-3 40A13 $a^{27}b^{10}$
$F_{41}$ 40A-13 $40$ $41$ $C_{40}$ 20A7 8A3 40A-13 $a^{13}b^{27}$
$F_{41}$ 40A17 $40$ $41$ $C_{40}$ 20A-3 8A1 40A17 $a^{23}b^{25}$
$F_{41}$ 40A-17 $40$ $41$ $C_{40}$ 20A3 8A-1 40A-17 $a^{17}b^{15}$
$F_{41}$ 40A19 $40$ $41$ $C_{40}$ 20A-1 8A3 40A19 $a^{21}b^{26}$
$F_{41}$ 40A-19 $40$ $41$ $C_{40}$ 20A1 8A-3 40A-19 $a^{19}b^{31}$
$F_{41}$ 41A $41$ $40$ $C_{41}$ 41A 41A 1A $b$
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