Galois group search results

Results (1-50 of 86 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
9T1	$C_9$	$9$	$1$	✓	$1$	$9$	$C_3$
9T2	$C_3^2$	$9$	$1$	✓	$1$	$9$	$C_3$ x 4
9T3	$D_{9}$	$18$	$1$	✓	$-1$	$6$	$S_3$	18T5
9T4	$S_3\times C_3$	$18$	$-1$	✓	$-1$	$9$	$C_3$, $S_3$	6T5, 18T3
9T5	$C_3^2:C_2$	$18$	$1$	✓	$-1$	$6$	$S_3$ x 4	18T4
9T6	$C_9:C_3$	$27$	$1$	✓	$2$	$11$	$C_3$	27T5
9T7	$C_3^2:C_3$	$27$	$1$	✓	$2$	$11$	$C_3$	9T7 x 3, 27T3
9T8	$S_3^2$	$36$	$-1$	✓	$-1$	$9$	$S_3$ x 2	6T9, 12T16, 18T9, 18T11 x 2, 36T13
9T9	$C_3^2:C_4$	$36$	$1$	✓	$-1$	$6$		6T10 x 2, 12T17 x 2, 18T10, 36T14
9T10	$(C_9:C_3):C_2$	$54$	$1$	✓	$-1$	$10$	$S_3$	18T18, 27T14
9T11	$C_3^2 : C_6$	$54$	$1$	✓	$-1$	$10$	$S_3$	9T13, 18T20, 18T21, 18T22, 27T11
9T12	$(C_3^2:C_3):C_2$	$54$	$-1$	✓	$-1$	$10$	$S_3$	9T12 x 3, 18T24 x 4, 27T6
9T13	$C_3^2 : S_3 $	$54$	$-1$	✓	$-1$	$10$	$C_3$	9T11, 18T20, 18T21, 18T22, 27T11
9T14	$C_3^2:Q_8$	$72$	$1$	✓	$-1$	$6$		12T47, 18T35 x 3, 24T82, 36T55
9T15	$C_3^2:C_8$	$72$	$-1$	✓	$-1$	$9$		12T46, 18T28, 24T81, 36T49
9T16	$S_3^2:C_2$	$72$	$-1$	✓	$-1$	$9$		6T13 x 2, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2
9T17	$C_3 \wr C_3 $	$81$	$1$	✓	$3$	$17$	$C_3$	9T17 x 2, 27T19, 27T21, 27T27 x 3
9T18	$C_3^2 : D_{6} $	$108$	$-1$	✓	$-1$	$11$	$S_3$	9T18, 18T51 x 2, 18T55 x 2, 18T56, 18T57 x 2, 27T29, 36T87 x 2, 36T90
9T19	$(C_3^2:C_8):C_2$	$144$	$-1$	✓	$-1$	$9$		12T84, 18T68, 18T71, 18T73, 24T278, 24T279, 24T280, 36T171, 36T172, 36T175
9T20	$C_3 \wr S_3 $	$162$	$-1$	✓	$-1$	$22$	$S_3$	9T20 x 2, 18T86 x 3, 27T37, 27T50 x 3, 27T70
9T21	$(C_3^3:C_3):C_2$	$162$	$1$	✓	$-1$	$13$	$S_3$	9T21 x 2, 18T88 x 3, 27T51 x 3, 27T52, 27T67
9T22	$(C_3^3:C_3):C_2$	$162$	$-1$	✓	$-1$	$13$	$C_3$	9T22 x 2, 18T85 x 3, 27T53 x 3, 27T62, 27T63
9T23	$(C_3^2:Q_8):C_3$	$216$	$1$	✓	$-1$	$10$		12T122, 24T562, 24T569, 27T82, 36T287, 36T309
9T24	$((C_3^3:C_3):C_2):C_2$	$324$	$-1$	✓	$-1$	$17$	$S_3$	9T24 x 2, 18T129 x 3, 18T136 x 3, 18T137 x 3, 27T121, 27T128 x 3, 27T129, 36T502 x 3
9T25	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$	$324$	$1$	✓	$-1$	$13$	$C_3$	12T132 x 2, 12T133, 18T141 x 2, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547
9T26	$((C_3^2:Q_8):C_3):C_2$	$432$	$-1$	✓	$-1$	$11$		12T157, 18T157, 24T1325, 24T1326, 24T1327, 24T1334, 27T139, 36T689, 36T709
9T27	$\PSL(2,8)$	$504$	$1$		$-1$	$9$		28T70, 36T712
9T28	$S_3 \wr C_3 $	$648$	$-1$	✓	$-1$	$17$	$C_3$	12T176, 18T197 x 2, 18T198 x 2, 18T202, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238
9T29	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$	$648$	$-1$	✓	$-1$	$17$	$S_3$	12T175, 18T219, 18T220, 18T223, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237
9T30	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$	$648$	$1$	✓	$-1$	$14$	$S_3$	12T177 x 2, 12T178, 18T217, 18T218, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240
9T31	$S_3\wr S_3$	$1296$	$-1$	✓	$-1$	$22$	$S_3$	12T213, 18T300, 18T303, 18T311, 18T312, 18T314, 18T315, 18T319, 18T320, 24T2893, 24T2894, 24T2895, 24T2912, 27T296, 27T298, 36T2197, 36T2198, 36T2199, 36T2201, 36T2202, 36T2210, 36T2211, 36T2212, 36T2213, 36T2214, 36T2215, 36T2216, 36T2217, 36T2218, 36T2219, 36T2220, 36T2225, 36T2226, 36T2229, 36T2305
9T32	$\mathrm{P}\Gamma\mathrm{L}(2,8)$	$1512$	$1$		$-1$	$11$		27T391, 28T165, 36T2342
9T33	$A_9$	$181440$	$1$		$-1$	$18$		36T23796
9T34	$S_9$	$362880$	$-1$		$-1$	$30$		18T887, 36T28590
10T1	$C_{10}$	$10$	$-1$	✓	$1$	$10$	$C_2$, $C_5$
10T2	$D_5$	$10$	$-1$	✓	$-1$	$4$	$C_2$, $D_{5}$	5T2
10T3	$D_{10}$	$20$	$-1$	✓	$-1$	$8$	$C_2$, $D_{5}$	10T3, 20T4
10T4	$F_5$	$20$	$-1$	✓	$-1$	$5$	$C_2$, $F_5$	5T3, 20T5
10T5	$F_{5}\times C_2$	$40$	$-1$	✓	$-1$	$10$	$C_2$, $F_5$	10T5, 20T9, 20T13, 40T14
10T6	$D_5\times C_5$	$50$	$-1$	✓	$-1$	$20$	$C_2$	10T6, 25T3
10T7	$A_{5}$	$60$	$1$		$-1$	$5$		5T4, 6T12, 12T33, 15T5, 20T15, 30T9
10T8	$C_2^4 : C_5$	$80$	$1$	✓	$-1$	$8$	$C_5$	10T8 x 2, 16T178, 20T17 x 6, 20T23, 40T57 x 3
10T9	$D_5^2$	$100$	$-1$	✓	$-1$	$16$	$C_2$	10T9, 20T28 x 2, 25T12
10T10	$C_5^2 : C_4$	$100$	$-1$	✓	$-1$	$10$	$C_2$	10T10, 20T27 x 2, 25T10
10T11	$A_5\times C_2$	$120$	$-1$		$-1$	$10$	$C_2$, $A_5$	12T75, 12T76, 20T31, 20T36, 24T203, 30T29, 30T30, 40T61
10T12	$S_5$	$120$	$-1$		$-1$	$7$	$C_2$, $S_5$	5T5, 6T14, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
10T13	$S_5$	$120$	$-1$		$-1$	$7$		5T5, 6T14, 10T12, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
10T14	$C_2 \times (C_2^4 : C_5)$	$160$	$-1$	✓	$-1$	$16$	$C_5$	10T14 x 2, 20T40 x 12, 20T41 x 6, 20T44 x 3, 20T46 x 3, 32T2133, 40T121 x 6, 40T122 x 6, 40T123 x 12, 40T141, 40T142 x 3
10T15	$(C_2^4 : C_5) : C_2$	$160$	$1$	✓	$-1$	$10$	$D_{5}$	10T15 x 2, 10T16 x 3, 16T415, 20T38 x 6, 20T39, 20T43 x 3, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146
10T16	$(C_2^4 : C_5) : C_2$	$160$	$-1$	✓	$-1$	$10$	$D_{5}$	10T15 x 3, 10T16 x 2, 16T415, 20T38 x 6, 20T39, 20T43 x 3, 20T45 x 3, 32T2132, 40T143 x 3, 40T144 x 3, 40T145 x 6, 40T146

 

Results are complete for degrees $\leq 23$.