Galois group search results

Results (40 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
17T9	$A_{17}$	$177843714048000$	$1$		$-1$	$156$
17T10	$S_{17}$	$355687428096000$	$-1$		$-1$	$297$
18T978	$A_9\wr C_2$	$65840947200$	$-1$		$-1$	$189$	$C_2$
18T979	$A_9^2.C_4$	$131681894400$	$1$		$-1$	$270$	$C_2$	36T116832
18T980	$A_9^2.C_2^2$	$131681894400$	$-1$		$-1$	$276$	$C_2$	36T116833
18T981	$S_9\wr C_2$	$263363788800$	$-1$		$-1$	$495$	$C_2$	36T117910, 36T117911, 36T117912
18T982	$A_{18}$	$3201186852864000$	$1$		$-1$	$200$
18T983	$S_{18}$	$6402373705728000$	$-1$		$-1$	$385$		36T120964
19T7	$A_{19}$	$60822550204416000$	$1$		$-1$	$254$
19T8	$S_{19}$	$121645100408832000$	$-1$		$-1$	$490$
20T1112	$A_{10}\wr C_2$	$6584094720000$	$1$		$-1$	$324$	$C_2$
20T1113	$A_{10}^2.C_4$	$13168189440000$	$-1$		$-1$	$504$	$C_2$	40T311850
20T1114	$A_{10}^2.C_2^2$	$13168189440000$	$1$		$-1$	$510$	$C_2$	40T311851
20T1115	$S_{10}\wr C_2$	$26336378880000$	$-1$		$-1$	$945$	$C_2$	40T312116, 40T312117, 40T312118
20T1116	$A_{20}$	$1216451004088320000$	$1$		$-1$	$324$
20T1117	$S_{20}$	$2432902008176640000$	$-1$		$-1$	$627$		40T315649
21T153	$A_7\wr C_3$	$48009024000$	$1$		$-1$	$267$	$C_3$	45T7189 x 2
21T154	$A_7^3.C_6$	$96018048000$	$-1$		$-1$	$333$	$C_3$	42T7458
21T155	$A_7^3.S_3$	$96018048000$	$1$		$-1$	$228$	$S_3$	42T7459
21T156	$A_7\wr S_3$	$96018048000$	$-1$		$-1$	$255$	$S_3$	42T7460, 45T7533 x 2
21T157	$A_7^3.D_6$	$192036096000$	$-1$		$-1$	$348$	$S_3$	42T7690, 42T7691, 42T7692
21T158	$A_7^3.A_4$	$192036096000$	$1$		$-1$	$587$	$C_3$	42T7693 x 2, 42T7694
21T159	$S_7\wr C_3$	$384072192000$	$-1$		$-1$	$1165$	$C_3$	42T7892 x 2, 42T7893, 42T7894 x 2, 42T7895, 42T7896
21T160	$A_7^3.S_4$	$384072192000$	$-1$		$-1$	$475$	$S_3$	42T7897, 42T7898, 42T7899
21T161	$A_7^3.S_4$	$384072192000$	$1$		$-1$	$472$	$S_3$	42T7900, 42T7901, 42T7902
21T162	$S_7\wr C_3.C_2$	$768144384000$	$-1$		$-1$	$920$	$S_3$	42T8089, 42T8090, 42T8091, 42T8092, 42T8093, 42T8094, 42T8095
21T163	$A_{21}$	$25545471085854720000$	$1$		$-1$	$408$
21T164	$S_{21}$	$51090942171709440000$	$-1$		$-1$	$792$		42T9215
22T50	$C_2^{10}.S_{11}$	$40874803200$	$-1$		$-1$	$376$	$S_{11}$	22T51, 44T1749
22T51	$C_2^{10}.S_{11}$	$40874803200$	$1$		$-1$	$376$	$S_{11}$	22T50, 44T1749
22T52	$C_2^{11}.A_{11}$	$40874803200$	$-1$		$-1$	$400$	$A_{11}$	44T1750
22T53	$C_2^{10}.(C_2\times S_{11})$	$81749606400$	$-1$		$-1$	$752$	$S_{11}$	22T53, 44T1774, 44T1777 x 2, 44T1778 x 2
22T54	$A_{11}\wr C_2$	$796675461120000$	$-1$		$-1$	$527$	$C_2$
22T55	$A_{11}^2.C_4$	$1593350922240000$	$1$		$-1$	$868$	$C_2$	44T1957
22T56	$A_{11}^2.C_2^2$	$1593350922240000$	$-1$		$-1$	$874$	$C_2$	44T1958
22T57	$S_{11}\wr C_2$	$3186701844480000$	$-1$		$-1$	$1652$	$C_2$	44T1966, 44T1967, 44T1968
22T58	$A_{22}$	$562000363888803840000$	$1$		$-1$	$513$
22T59	$S_{22}$	$1124000727777607680000$	$-1$		$-1$	$1002$		44T2028
23T6	$A_{23}$	$12926008369442488320000$	$1$		$-1$	$641$
23T7	$S_{23}$	$25852016738884976640000$	$-1$		$-1$	$1255$		46T44

 

Results are complete for degrees $\leq 23$.