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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 $C_2$ $W(B_{1})$ $2$ $2$ 2 $C_2$ $C_1$ $C_1$ $C_{2}$ Cyclic
8.3 $D_4$ $W(B_{2})$ $2^{3}$ $2^{2}$ 5 $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
48.48 $C_2\times S_4$ $W(B_{3})$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ 10 $C_2$ $S_4$ $A_4$ $C_{2}^{2}$ Solvable - 3
384.5602 $C_2\wr S_4$ $W(B_{4})$ $2^{7} \cdot 3$ $2^{3} \cdot 3$ 20 $C_2$ $C_2^3:S_4$ $Q_8:A_4$ $C_{2}^{2}$ Solvable - 4
3840.ch $C_2\wr S_5$ $W(B_{5})$ $2^{8} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 36 $C_2$ $C_2^4:S_5$ $C_2^4:A_5$ $C_{2}^{2}$ Non-Solvable - 7
46080.c $C_2^6.S_6$ $W(B_{6})$ $2^{10} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 65 $C_2$ $C_2^5:S_6$ $C_2^5:A_6$ $C_{2}^{2}$ Non-Solvable - 8
645120.a $C_2^7.S_7$ $W(B_{7})$ $2^{11} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ 110 $C_2$ $C_2^6.S_7$ $C_2^6:A_7$ $C_{2}^{2}$ Non-Solvable - 9
10321920.a $C_2^8.S_8$ $W(B_{8})$ $2^{15} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ 185 $C_2$ $C_2^7.S_8$ $C_2^7.A_8$ $C_{2}^{2}$ Non-Solvable - 10
185794560.a $C_2^9.S_9$ $W(B_{9})$ $2^{16} \cdot 3^{4} \cdot 5 \cdot 7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ 300 $C_2$ $C_2^8.S_9$ $C_2^8.A_9$ $C_{2}^{2}$ Non-Solvable - 11
3715891200.a $C_2^{10}.S_{10}$ $W(B_{10})$ $2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ 481 $C_2$ $C_2^9.S_{10}$ $C_2^9.A_{10}$ $C_{2}^{2}$ Non-Solvable - 12
81749606400.a $C_2^{10}.(C_2\times S_{11})$ $W(B_{11})$ $2^{19} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ 752 $C_2$ $C_2^{10}.S_{11}$ $C_2^{10}.A_{11}$ $C_{2}^{2}$ Non-Solvable - 13
1961990553600.a $C_2^{12}.S_{12}$ $W(B_{12})$ $2^{22} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ 1165 $C_2$ $C_2^{11}.A_{12}$ $C_{2}^{2}$ Non-Solvable - 14
51011754393600.a $C_2^{12}.(C_2\times S_{13})$ $W(B_{13})$ $2^{23} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 1770 $C_2$ $C_2^{12}.S_{13}$ $C_2^{12}.A_{13}$ $C_{2}^{2}$ Non-Solvable - 15
1428329123020800.a $C_2^{14}.A_{14}.C_2$ $W(B_{14})$ $2^{25} \cdot 3^{5} \cdot 5^{2} \cdot 7^{2} \cdot 11 \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 2665 $C_2$ $C_2^{13}.A_{14}$ $C_{2}^{2}$ Non-Solvable - 16
42849873690624000.a $C_2^{15}.A_{15}.C_2$ $W(B_{15})$ $2^{26} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 3956 $C_2$ $C_2^{14}.A_{15}.C_2$ $C_2^{14}.A_{15}$ $C_{2}^{2}$ Non-Solvable - 17
1371195958099968000.a $C_2^{16}.A_{16}.C_2$ $W(B_{16})$ $2^{31} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13$ 5822 $C_2$ $C_2^{15}.A_{16}$ $C_{2}^{2}$ Non-Solvable - 18
46620662575398912000.a $C_2^{17}.A_{17}.C_2$ $W(B_{17})$ $2^{32} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17$ 8470 $C_2$ $C_2^{16}.A_{17}.C_2$ $C_2^{16}.A_{17}$ $C_{2}^{2}$ Non-Solvable - 19
1678343852714360832000.a $C_2^{18}.A_{18}.C_2$ $W(B_{18})$ $2^{34} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17$ 12230 $C_2$ $C_2^{17}.A_{18}$ $C_{2}^{2}$ Non-Solvable - 20
63777066403145711616000.a $C_2^{19}.A_{19}.C_2$ $W(B_{19})$ $2^{35} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 17490 $C_2$ $C_2^{18}.A_{19}.C_2$ $C_2^{18}.A_{19}$ $C_{2}^{2}$ Non-Solvable - 21
2551082656125828464640000.a $C_2^{20}.A_{20}.C_2$ $W(B_{20})$ $2^{38} \cdot 3^{8} \cdot 5^{4} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 24842 $C_2$ $C_2^{19}.A_{20}$ $C_{2}^{2}$ Non-Solvable - 22
107145471557284795514880000.a $C_2^{21}.A_{21}.C_2$ $W(B_{21})$ $2^{39} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11 \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 35002 $C_2$ $C_2^{20}.A_{21}.C_2$ $C_2^{20}.A_{21}$ $C_{2}^{2}$ Non-Solvable - 23
4714400748520531002654720000.a $C_2^{22}.A_{22}.C_2$ $W(B_{22})$ $2^{41} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ 49010 $C_2$ $C_{2}^{2}$ Non-Solvable - 24
216862434431944426122117120000.a $C_2^{23}.A_{23}.C_2$ $W(B_{23})$ $2^{42} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23$ 68150 $C_2$ $C_{2}^{2}$ Non-Solvable - 25
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