Galois group search results

Results (1-50 of 408617 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
9T33	$A_9$	$181440$	$1$		$-1$	$18$		36T23796
9T34	$S_9$	$362880$	$-1$		$-1$	$30$		18T887, 36T28590
10T44	$A_{10}$	$1814400$	$1$		$-1$	$24$		45T1982
10T45	$S_{10}$	$3628800$	$-1$		$-1$	$42$		20T1007, 45T2246
11T7	$A_{11}$	$19958400$	$1$		$-1$	$31$
11T8	$S_{11}$	$39916800$	$-1$		$-1$	$56$		22T45
12T294	$A_4^3.(C_2\times S_4)$	$82944$	$-1$	✓	$-1$	$65$	$S_3$	18T770, 18T773, 18T776, 18T777, 18T779, 18T780, 18T783, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423
12T295	$M_{12}$	$95040$	$1$		$-1$	$15$		12T295
12T296	$A_6\wr C_2$	$259200$	$1$		$-1$	$35$	$C_2$	12T296, 20T888, 30T1681 x 2, 36T25180 x 2, 40T107011
12T297	$A_6^2:C_2^2$	$518400$	$1$		$-1$	$49$	$C_2$	12T297, 20T934, 24T20411 x 2, 30T1851 x 2, 36T30378 x 2, 40T139782 x 2, 40T139783
12T298	$A_6^2:C_4$	$518400$	$-1$		$-1$	$46$	$C_2$	12T298, 20T937, 24T20412 x 2, 30T1854 x 2, 36T30377 x 2, 40T139787, 40T139788 x 2
12T299	$S_6\wr C_2$	$1036800$	$-1$		$-1$	$77$	$C_2$	12T299, 20T973, 24T21434 x 2, 24T21435 x 2, 24T21436 x 2, 30T2029 x 2, 36T36499 x 2, 40T148363 x 2, 40T148364, 40T148365 x 2, 40T148366, 40T148367
12T300	$A_{12}$	$239500800$	$1$		$-1$	$43$
12T301	$S_{12}$	$479001600$	$-1$		$-1$	$77$		24T24748
13T8	$A_{13}$	$3113510400$	$1$		$-1$	$55$
13T9	$S_{13}$	$6227020800$	$-1$		$-1$	$101$		26T83
14T53	$C_2^6:A_7$	$161280$	$1$		$-1$	$32$	$A_7$	42T1346, 42T1347
14T54	$C_2^6.S_7$	$322560$	$-1$		$-1$	$55$	$S_7$	14T55, 28T945, 42T1589, 42T1590, 42T1591, 42T1592
14T55	$C_2^6.S_7$	$322560$	$1$		$-1$	$55$	$S_7$	14T54, 28T945, 42T1589, 42T1590, 42T1591, 42T1592
14T56	$C_2^7.A_7$	$322560$	$-1$		$-1$	$64$	$A_7$	28T946, 42T1587, 42T1588
14T57	$C_2^7.S_7$	$645120$	$-1$		$-1$	$110$	$S_7$	14T57, 28T1097 x 2, 28T1098, 28T1099 x 2, 42T1778 x 2, 42T1779 x 2
14T58	$A_7\wr C_2$	$12700800$	$-1$		$-1$	$54$	$C_2$	30T3274 x 2, 42T2726
14T59	$A_7^2.C_4$	$25401600$	$1$		$-1$	$78$	$C_2$	28T1575, 42T2989
14T60	$A_7^2.C_2^2$	$25401600$	$-1$		$-1$	$81$	$C_2$	28T1576, 42T2990
14T61	$S_7\wr C_2$	$50803200$	$-1$		$-1$	$135$	$C_2$	28T1634, 28T1635, 28T1636, 42T3347
15T84	$C_3:S_3^4:F_5$	$77760$	$1$	✓	$-1$	$39$	$F_5$	30T1334, 30T1340, 30T1342
15T85	$C_3:S_3^4:F_5$	$77760$	$-1$	✓	$-1$	$45$	$F_5$	30T1341, 30T1343, 30T1350
15T86	$S_3\wr D_5$	$77760$	$-1$	✓	$-1$	$72$	$D_{5}$	30T1344, 30T1345 x 2, 30T1346, 30T1347, 30T1348 x 2, 30T1355, 30T1356, 30T1357, 30T1362 x 2, 30T1364, 30T1365 x 2, 30T1367 x 2, 45T935 x 2
15T87	$S_3\wr F_5$	$155520$	$-1$	✓	$-1$	$63$	$F_5$	30T1538, 30T1540, 30T1549, 30T1550, 30T1557, 30T1558, 30T1559
15T88	$C_3:S_3^4:A_5$	$233280$	$1$		$-1$	$48$	$A_5$	30T1643, 30T1647, 45T1278
15T89	$C_3:S_3^4:S_5$	$466560$	$1$		$-1$	$60$	$S_5$	30T1810, 30T1824, 30T1833, 30T1834, 45T1514
15T90	$S_3\wr A_5$	$466560$	$-1$		$-1$	$72$	$A_5$	30T1811, 30T1820, 30T1823, 30T1827, 45T1509
15T91	$C_3:S_3^4:S_5$	$466560$	$-1$		$-1$	$72$	$S_5$	30T1814, 30T1822, 30T1825, 30T1829, 45T1513
15T92	$A_5\wr C_3$	$648000$	$1$		$-1$	$55$	$C_3$	18T911, 30T1895, 36T33201, 45T1672
15T93	$S_3^5.S_5$	$933120$	$-1$		$-1$	$108$	$S_5$	30T1990, 30T1993, 30T1995, 30T2002, 30T2006, 30T2009, 30T2010, 30T2011, 45T1750
15T94	$A_5^3:S_3$	$1296000$	$1$		$-1$	$50$	$S_3$	18T935, 30T2087, 30T2093, 36T39374, 45T1883
15T95	$A_5^3:C_6$	$1296000$	$-1$		$-1$	$53$	$C_3$	18T933, 30T2088, 30T2090, 36T39370, 45T1884
15T96	$A_5\wr S_3$	$1296000$	$-1$		$-1$	$65$	$S_3$	18T934, 30T2089, 30T2091, 36T39371, 36T39372, 36T39373, 45T1885
15T97	$A_5^3:D_6$	$2592000$	$-1$		$-1$	$70$	$S_3$	18T946, 30T2327, 30T2331, 30T2332, 30T2333, 36T46223, 36T46224, 36T46225, 45T2114
15T98	$A_5^3.A_4$	$2592000$	$1$		$-1$	$71$	$C_3$	18T947, 30T2335 x 2, 30T2336, 30T2337, 36T46226, 36T46227 x 2, 45T2115
15T99	$A_5^3.S_4$	$5184000$	$1$		$-1$	$76$	$S_3$	18T954, 30T2624, 30T2625, 30T2627, 30T2628, 36T53415, 36T53416, 36T53417, 45T2363
15T100	$A_5^3.S_4$	$5184000$	$-1$		$-1$	$79$	$S_3$	18T955, 30T2610, 30T2612, 30T2614, 30T2619, 36T53418, 36T53419, 36T53420, 45T2364
15T101	$S_5\wr C_3$	$5184000$	$-1$		$-1$	$133$	$C_3$	18T953, 30T2611, 30T2615, 30T2621 x 2, 30T2630 x 2, 30T2632, 30T2634, 36T53410 x 2, 36T53411, 36T53412 x 2, 36T53413, 36T53414, 45T2365
15T102	$S_5^3.S_3$	$10368000$	$-1$		$-1$	$140$	$S_3$	18T958, 30T2981, 30T2984, 30T2985, 30T2986, 30T2989, 30T2990, 30T2994, 30T2998, 36T60049, 36T60050, 36T60051, 36T60052, 36T60053, 36T60054, 36T60055, 45T2638
16T1862	$C_2^8.A_4\wr C_2$	$73728$	$-1$	✓	$-1$	$152$	$C_2$, $A_4\wr C_2$	16T1862 x 3, 32T1831766 x 2, 32T1831767 x 2, 32T1831768 x 2, 32T1831936 x 2
16T1863	$C_2^7.\PGOPlus(4,3)$	$73728$	$-1$	✓	$-1$	$89$	$C_2$, $(A_4\wr C_2):C_2$	16T1863 x 3, 32T1831769 x 2, 32T1831770 x 2, 32T1831771 x 2, 32T1831893 x 2
16T1864	$C_2^8.D_6\wr C_2$	$73728$	$1$	✓	$-1$	$119$	$C_2$, $D_{4}$	16T1864, 24T16233 x 2, 24T16234 x 2, 24T16235 x 2, 24T16236 x 2, 24T16237 x 2, 24T16238 x 2, 24T16239 x 2, 24T16240 x 2, 24T16365 x 2, 24T16367 x 2, 24T16369 x 2, 24T16371 x 2, 24T16513 x 2, 24T16515 x 2, 24T16517 x 2, 24T16519 x 2, 32T1831704, 32T1831772 x 2, 32T1831773 x 2, 32T1831774 x 2, 32T1831775 x 2, 32T1831776 x 2, 32T1831777 x 2, 32T1831778 x 2
16T1865	$C_2^7.A_4^2:C_4$	$73728$	$1$	✓	$-1$	$83$	$C_2$, $A_4^2:C_4$	16T1865 x 3, 32T1831779 x 2, 32T1831780 x 2, 32T1831781 x 2, 32T1831881 x 2
16T1866	$C_2^7.A_4^2:C_4$	$73728$	$-1$	✓	$-1$	$83$	$C_2$, $A_4^2:C_4$	16T1866 x 3, 32T1831782 x 2, 32T1831783 x 2, 32T1831784 x 2, 32T1831906 x 2
16T1867	$C_2^7.\PGOPlus(4,3)$	$73728$	$1$	✓	$-1$	$101$	$C_2$, $(A_4\wr C_2):C_2$	16T1867 x 3, 32T1831785 x 2, 32T1831786 x 2, 32T1831787 x 2, 32T1831900 x 2

 

Results are complete for degrees $\leq 23$.