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Order Exponent Nilpotency class Nilpotent
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Results (23 matches)

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Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
2.1 $C_2$ $W(D_{1})$ $2$ $2$ 2 $C_2$ $C_1$ $C_1$ $C_{2}$ Cyclic
4.2 $C_2^2$ $W(D_{2})$ $2^{2}$ $2$ 4 $C_2^2$ $C_1$ $C_1$ $C_{2}^{2}$ Abelian - 2
24.12 $S_4$ $W(D_{3})$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ 5 $C_1$ $S_4$ $A_4$ $C_{2}$ Solvable - 3
192.1493 $C_2^3:S_4$ $W(D_{4})$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ 13 $C_2$ $C_2^2:S_4$ $Q_8:A_4$ $C_{2}$ Solvable - 4
1920.240996 $C_2^4:S_5$ $W(D_{5})$ $2^{7} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 18 $C_1$ $C_2^4:S_5$ $C_2^4:A_5$ $C_{2}$ Non-Solvable - 6
23040.n $C_2^5:S_6$ $W(D_{6})$ $2^{9} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 37 $C_2$ $C_2^4:S_6$ $C_2^5:A_6$ $C_{2}$ Non-Solvable - 7
322560.b $C_2^6.S_7$ $W(D_{7})$ $2^{10} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ 55 $C_1$ $C_2^6.S_7$ $C_2^6:A_7$ $C_{2}$ Non-Solvable - 8
5160960.b $C_2^7.S_8$ $W(D_{8})$ $2^{14} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ 100 $C_2$ $C_2^7.A_8$ $C_{2}$ Non-Solvable - 9
92897280.b $C_2^8.S_9$ $W(D_{9})$ $2^{15} \cdot 3^{4} \cdot 5 \cdot 7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ 150 $C_1$ $C_2^8.S_9$ $C_2^8.A_9$ $C_{2}$ Non-Solvable - 10
1857945600.b $C_2^9.S_{10}$ $W(D_{10})$ $2^{17} \cdot 3^{4} \cdot 5^{2} \cdot 7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ 251 $C_2$ $C_2^9.A_{10}$ $C_{2}$ Non-Solvable - 11
40874803200.a $C_2^{10}.S_{11}$ $W(D_{11})$ $2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ 376 $C_1$ $C_2^{10}.S_{11}$ $C_2^{10}.A_{11}$ $C_{2}$ Non-Solvable - 12
980995276800.b $C_2^{11}.A_{12}.C_2$ $W(D_{12})$ $2^{21} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ 599 $C_2$ $C_2^{11}.A_{12}$ $C_{2}$ Non-Solvable - 13
25505877196800.a $C_2^{12}.S_{13}$ $W(D_{13})$ $2^{22} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 885 $C_1$ $C_2^{12}.S_{13}$ $C_2^{12}.A_{13}$ $C_{2}$ Non-Solvable - 14
714164561510400.b $C_2^{13}.A_{14}.C_2$ $W(D_{14})$ $2^{24} \cdot 3^{5} \cdot 5^{2} \cdot 7^{2} \cdot 11 \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 1355 $C_2$ $C_2^{13}.A_{14}$ $C_{2}$ Non-Solvable - 15
21424936845312000.a $C_2^{14}.A_{15}.C_2$ $W(D_{15})$ $2^{25} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 1978 $C_1$ $C_2^{14}.A_{15}.C_2$ $C_2^{14}.A_{15}$ $C_{2}$ Non-Solvable - 16
685597979049984000.a $C_2^{15}.A_{16}.C_2$ $W(D_{16})$ $2^{30} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 2944 $C_2$ $C_2^{15}.A_{16}$ $C_{2}$ Non-Solvable - 17
23310331287699456000.b $C_2^{16}.A_{17}.C_2$ $W(D_{17})$ $2^{31} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17$ 4235 $C_1$ $C_2^{16}.A_{17}.C_2$ $C_2^{16}.A_{17}$ $C_{2}$ Non-Solvable - 18
839171926357180416000.c $C_2^{17}.A_{18}.C_2$ $W(D_{18})$ $2^{33} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17$ 6160 $C_2$ $C_2^{17}.A_{18}$ $C_{2}$ Non-Solvable - 19
31888533201572855808000.b $C_2^{18}.A_{19}.C_2$ $W(D_{19})$ $2^{34} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 8745 $C_1$ $C_2^{18}.A_{19}.C_2$ $C_2^{18}.A_{19}$ $C_{2}$ Non-Solvable - 20
1275541328062914232320000.b $C_2^{19}.A_{20}.C_2$ $W(D_{20})$ $2^{37} \cdot 3^{8} \cdot 5^{4} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 12484 $C_2$ $C_2^{19}.A_{20}$ $C_{2}$ Non-Solvable - 21
53572735778642397757440000.b $C_2^{20}.A_{21}.C_2$ $W(D_{21})$ $2^{38} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11 \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 17501 $C_1$ $C_2^{20}.A_{21}.C_2$ $C_2^{20}.A_{21}$ $C_{2}$ Non-Solvable - 22
2357200374260265501327360000.b $C_2^{21}.A_{22}.C_2$ $W(D_{22})$ $2^{40} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 24589 $C_2$ $C_{2}$ Non-Solvable - 23
108431217215972213061058560000.b $C_2^{22}.A_{23}.C_2$ $W(D_{23})$ $2^{41} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23$ 34075 $C_1$ $C_2^{22}.A_{23}.C_2$ $C_2^{22}.A_{23}$ $C_{2}$ Non-Solvable - 24
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