Galois group search results

Results (1-50 of 542 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
17T6	$\PSL(2,16)$	$4080$	$1$		$-1$	$17$
17T7	$\PSL(2,16):C_2$	$8160$	$1$		$-1$	$16$
17T8	$\PSL(2,16):C_4$	$16320$	$1$		$-1$	$17$
17T9	$A_{17}$	$177843714048000$	$1$		$-1$	$156$
17T10	$S_{17}$	$355687428096000$	$-1$		$-1$	$297$
18T90	$\GL(2,4)$	$180$	$1$		$-1$	$15$	$C_3$, $\PSL(2,5)$	15T15 x 2, 15T16, 30T45, 36T176, 45T16
18T144	$C_3\times S_5$	$360$	$-1$		$-1$	$21$	$C_3$, $\PGL(2,5)$	15T24, 30T90, 30T98, 30T103, 36T550, 45T44
18T145	$S_3\times A_5$	$360$	$1$		$-1$	$15$	$S_3$, $\PSL(2,5)$	15T23, 30T85, 30T94, 30T102, 36T551, 36T552, 36T553, 45T40
18T146	$C_3:S_5$	$360$	$-1$		$-1$	$12$	$S_3$, $\PGL(2,5)$	15T21 x 2, 15T22, 30T89, 30T93 x 2, 30T101, 36T554, 45T45
18T227	$S_3\times S_5$	$720$	$-1$		$-1$	$21$	$S_3$, $\PGL(2,5)$	15T29, 30T165, 30T167, 30T170, 30T174, 30T178, 36T1249, 36T1250, 36T1251, 45T94
18T260	$C_2\times \SL(2,8)$	$1008$	$-1$		$-1$	$18$	$C_2$, $\PSL(2,8)$
18T261	$C_3\times A_6$	$1080$	$1$		$-1$	$21$	$C_3$, $A_6$	18T261, 30T223, 45T149 x 2
18T262	$C_3.A_6$	$1080$	$1$		$-1$	$17$	$A_6$	18T262, 45T150 x 2
18T362	$C_3\times S_6$	$2160$	$-1$		$-1$	$33$	$C_3$, $S_6$	18T362, 30T361, 36T3026 x 2, 45T228 x 2
18T363	$S_3\times A_6$	$2160$	$1$		$-1$	$21$	$S_3$, $A_6$	18T363, 30T358, 36T3027 x 2, 45T221 x 2
18T364	$C_3:S_6$	$2160$	$-1$		$-1$	$18$	$S_3$, $S_6$	18T364, 30T362, 36T3028 x 2, 45T226 x 2
18T365	$C_3.S_6$	$2160$	$-1$		$-1$	$16$	$S_6$	18T365, 36T3029 x 2, 45T227 x 2
18T377	$\PSL(2,17)$	$2448$	$1$		$-1$	$11$		36T3474
18T427	$\SL(2,8):C_6$	$3024$	$-1$		$-1$	$22$	$C_2$, $\mathrm{P}\Gamma\mathrm{L}(2,8)$
18T452	$S_3\times S_6$	$4320$	$-1$		$-1$	$33$	$S_3$, $S_6$	18T452, 30T535, 36T4986 x 2, 36T4987 x 2, 36T4988 x 2, 45T330 x 2
18T468	$\PGL(2,17)$	$4896$	$-1$		$-1$	$19$		36T5561
18T596	$C_3^5:A_5$	$14580$	$1$		$-1$	$48$	$\PSL(2,5)$	36T9863, 45T551, 45T573 x 3
18T664	$C_3^5:S_5$	$29160$	$-1$		$-1$	$48$	$\PGL(2,5)$	36T13311, 45T694, 45T726
18T665	$C_3^5:(C_2\times A_5)$	$29160$	$1$		$-1$	$36$	$\PSL(2,5)$	36T13312, 36T13313, 36T13314, 45T686, 45T724
18T666	$C_3^5:S_5$	$29160$	$-1$		$-1$	$48$	$\PGL(2,5)$	36T13315, 45T693, 45T725 x 3
18T722	$C_3\wr A_5$	$43740$	$1$		$-1$	$120$	$\PSL(2,5)$	18T722 x 2, 36T15827 x 3, 45T799 x 3
18T723	$C_3^6:A_5$	$43740$	$1$		$-1$	$53$	$\PSL(2,5)$	18T723 x 3, 30T1167 x 8, 30T1168 x 4, 36T15828 x 4, 45T802 x 4
18T736	$C_3^5:(C_2\times S_5)$	$58320$	$-1$		$-1$	$48$	$\PGL(2,5)$	36T17155, 36T17156, 36T17157, 45T866, 45T881
18T787	$C_3\wr S_5$	$87480$	$-1$		$-1$	$120$	$\PGL(2,5)$	18T787 x 2, 36T19445 x 3, 45T973 x 3
18T788	$C_3^6:(C_2\times A_5)$	$87480$	$1$		$-1$	$70$	$\PSL(2,5)$	18T788 x 3, 30T1385 x 4, 36T19446 x 4, 36T19447 x 4, 36T19448 x 4, 45T969 x 4
18T789	$C_3^6:S_5$	$87480$	$-1$		$-1$	$84$	$\PGL(2,5)$	18T789 x 2, 36T19449 x 3, 45T974 x 3
18T790	$C_3^6:(C_2\times A_5)$	$87480$	$1$		$-1$	$72$	$\PSL(2,5)$	18T790 x 2, 36T19450 x 3, 36T19451 x 3, 36T19452 x 3, 45T967 x 3
18T791	$C_3^5:A_6$	$87480$	$1$		$-1$	$47$	$A_6$	45T987
18T802	$C_2^8:\SL(2,8)$	$129024$	$1$		$-1$	$29$	$\PSL(2,8)$
18T845	$C_3\wr S_5:C_2$	$174960$	$-1$		$-1$	$84$	$\PGL(2,5)$	18T845 x 2, 36T23778 x 3, 36T23779 x 3, 36T23780 x 3, 45T1169 x 3
18T846	$C_3^6:A_5:C_4$	$174960$	$1$		$-1$	$56$	$\PGL(2,5)$	18T846, 36T23781 x 2, 36T23782 x 2, 36T23783 x 2, 36T23787
18T847	$C_3^5:S_6$	$174960$	$-1$		$-1$	$79$	$S_6$	36T23784, 45T1179
18T848	$C_3^5:S_6$	$174960$	$-1$		$-1$	$46$	$S_6$	36T23785, 45T1178
18T849	$C_3^5:(C_2\times A_6)$	$174960$	$1$		$-1$	$43$	$A_6$	36T23786, 45T1172
18T855	$C_2^9.\PSL(2,8)$	$258048$	$-1$		$-1$	$58$	$\PSL(2,8)$	36T25167
18T856	$C_3\wr A_6$	$262440$	$1$		$-1$	$133$	$A_6$	18T856 x 2, 45T1296 x 3
18T886	$C_3^5:(C_2\times S_6)$	$349920$	$-1$		$-1$	$74$	$S_6$	36T28585, 36T28586, 36T28587, 45T1429
18T887	$S_9$	$362880$	$-1$		$-1$	$30$	$C_2$, $S_9$	9T34, 36T28590
18T888	$C_2\times A_9$	$362880$	$-1$		$-1$	$36$	$C_2$, $A_9$
18T890	$C_2^8:{}^2G(2,3)$	$387072$	$1$		$-1$	$39$	$\mathrm{P}\Gamma\mathrm{L}(2,8)$
18T897	$\SOPlus(4,8)$	$508032$	$-1$		$-1$	$54$	$C_2$
18T898	$C_3\wr S_6$	$524880$	$-1$		$-1$	$221$	$S_6$	18T898 x 2, 36T30380 x 3, 45T1526 x 3
18T899	$C_3^6:S_6$	$524880$	$-1$		$-1$	$89$	$S_6$	18T899 x 2, 36T30381 x 3, 45T1525 x 3
18T900	$C_3\wr A_6:C_2$	$524880$	$1$		$-1$	$86$	$A_6$	18T900 x 2, 36T30382 x 3, 45T1520 x 3
18T911	$A_5\wr C_3$	$648000$	$1$		$-1$	$55$	$C_3$	15T92, 30T1895, 36T33201, 45T1672

 

Results are complete for degrees $\leq 23$.