Galois group search results

Results (1-50 of 3169 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
7T5	$\GL(3,2)$	$168$	$1$		$-1$	$6$		7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
8T35	$C_2 \wr C_2\wr C_2$	$128$	$-1$	✓	$4$	$20$	$C_2$, $D_{4}$	8T35 x 7, 16T376 x 4, 16T388 x 4, 16T390 x 4, 16T391 x 4, 16T393 x 4, 16T395 x 4, 16T396 x 4, 16T401 x 4, 32T852 x 4, 32T853 x 2, 32T854 x 2, 32T872 x 2, 32T876 x 4, 32T877 x 2, 32T880 x 2, 32T882 x 2, 32T883 x 4, 32T884 x 2, 32T885 x 2
8T36	$C_2^3:(C_7: C_3)$	$168$	$1$	✓	$-1$	$8$		14T11, 24T283, 28T27, 42T26
8T37	$\PSL(2,7)$	$168$	$1$		$-1$	$6$		7T5 x 2, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
8T38	$C_2\wr A_4$	$192$	$-1$	✓	$-1$	$16$	$A_4$	8T38, 16T425, 16T427, 24T288 x 2, 24T425 x 2, 32T2185 x 2
8T39	$C_2^3:S_4$	$192$	$1$	✓	$-1$	$13$	$S_4$	8T39 x 5, 16T442 x 3, 24T333 x 6, 24T431 x 2, 32T2213 x 2
8T40	$Q_8:S_4$	$192$	$-1$	✓	$-1$	$13$	$S_4$	8T40, 16T444, 16T445, 24T332 x 2, 24T430 x 2, 32T2215 x 2
8T41	$V_4^2:(S_3\times C_2)$	$192$	$1$	✓	$-1$	$14$	$C_2$	8T41, 12T108 x 2, 12T109 x 2, 12T110 x 2, 12T111 x 2, 16T435 x 2, 16T436, 24T516 x 2, 24T517 x 2, 24T518 x 2, 24T519 x 2, 24T520 x 2, 24T521 x 2, 24T522 x 2, 24T523, 24T524 x 2, 24T525 x 2, 24T526 x 2, 24T527, 24T528, 24T529, 32T2148, 32T2149 x 2
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
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
10T17	$(C_5^2 : C_4) : C_2$	$200$	$-1$	✓	$-1$	$14$	$C_2$	10T17, 20T54 x 2, 25T19, 40T169 x 2
10T18	$C_5^2 : C_8$	$200$	$1$	✓	$-1$	$11$	$C_2$	10T18 x 2, 20T56 x 3, 25T20, 40T171 x 3
10T19	$D_5^2 : C_2$	$200$	$-1$	✓	$-1$	$14$	$C_2$	10T21 x 2, 20T48 x 2, 20T50 x 2, 20T55, 20T57 x 2, 25T21, 40T167 x 2, 40T170
10T20	$C_5^2 : Q_8$	$200$	$-1$	✓	$-1$	$8$	$C_2$	10T20 x 2, 20T47 x 3, 25T17, 40T166 x 3
10T21	$D_5^2 : C_2$	$200$	$-1$	✓	$-1$	$14$	$C_2$	10T19, 10T21, 20T48 x 2, 20T50 x 2, 20T55, 20T57 x 2, 25T21, 40T167 x 2, 40T170
10T22	$S_5\times C_2$	$240$	$-1$		$-1$	$14$	$C_2$, $S_5$	10T22, 12T123 x 2, 20T62 x 2, 20T65 x 2, 20T70, 24T570, 24T577, 30T58 x 2, 30T60 x 2, 40T173 x 2, 40T180, 40T181, 40T187 x 2
12T77	$S_3^2:C_2^2$	$144$	$1$	✓	$-1$	$18$	$C_2$ x 3, $C_2^2$, $C_3^2:D_4$	12T77 x 3, 12T78 x 4, 18T63 x 4, 24T261 x 4, 24T262 x 4, 24T263 x 2, 24T264 x 2, 36T157 x 2, 36T159 x 4, 36T165 x 2
12T78	$S_3^2:C_2^2$	$144$	$-1$	✓	$-1$	$18$	$C_2$, $D_{4}$, $C_3^2:D_4$	12T77 x 4, 12T78 x 3, 18T63 x 4, 24T261 x 4, 24T262 x 4, 24T263 x 2, 24T264 x 2, 36T157 x 2, 36T159 x 4, 36T165 x 2
12T79	$S_3^2:C_4$	$144$	$-1$	✓	$-1$	$18$	$C_2$, $C_4$, $C_3^2:D_4$	12T79, 12T80 x 2, 24T213, 24T215, 24T265 x 2, 24T266 x 2, 24T267, 24T268, 36T156 x 2, 36T158, 36T164
12T80	$S_3^2:C_4$	$144$	$-1$	✓	$-1$	$18$	$C_2$, $D_{4}$, $C_3^2:D_4$	12T79 x 2, 12T80, 24T213, 24T215, 24T265 x 2, 24T266 x 2, 24T267, 24T268, 36T156 x 2, 36T158, 36T164
12T81	$D_6:D_6$	$144$	$-1$	✓	$-1$	$24$	$C_2$, $D_{4}$, $S_3^2$	12T81 x 3, 24T269 x 2, 24T270 x 2, 24T271 x 2, 36T123 x 2, 36T147 x 2
12T82	$C_6^2:C_4$	$144$	$-1$	✓	$-1$	$18$	$C_2$, $D_{4}$, $C_3^2:C_4$	12T82 x 7, 24T272 x 4, 24T273 x 4, 24T274 x 4, 36T126 x 2, 36T141 x 2
12T83	$S_3\times S_4$	$144$	$-1$	✓	$-1$	$15$	$S_3$, $S_4$	18T65, 18T69, 18T70, 18T72, 24T275, 24T276, 24T277, 24T281, 36T124, 36T125, 36T128, 36T129, 36T130, 36T131, 36T173, 36T174
12T84	$F_9:C_2$	$144$	$1$	✓	$-1$	$9$	$C_2$, $D_{4}$	9T19, 18T68, 18T71, 18T73, 24T278, 24T279, 24T280, 36T171, 36T172, 36T175
12T85	$A_4^2$	$144$	$1$	✓	$-1$	$16$	$C_3$	12T85, 16T414, 18T62, 24T212 x 2, 36T121, 36T122 x 2, 36T170 x 2
12T86	$D_4\times S_4$	$192$	$-1$	✓	$-1$	$25$	$C_2$, $S_3$, $D_{6}$	12T86 x 3, 16T421 x 4, 24T358 x 2, 24T393 x 2, 24T434 x 2, 24T435 x 2, 24T436 x 2, 24T437 x 4, 24T438 x 4, 24T439 x 4, 24T440 x 4, 32T2138 x 2, 32T2139 x 2, 32T2140 x 2
12T87	$C_2^4:A_4$	$192$	$1$	✓	$-1$	$20$	$C_2$, $C_3$, $C_6$	12T87, 12T88 x 2, 16T416 x 2, 24T441 x 2, 24T442 x 2, 24T443 x 4, 24T444 x 2, 24T445 x 2, 24T446 x 2, 24T447 x 2, 24T448 x 4, 24T449, 24T450, 24T451 x 4, 24T452 x 4, 32T2183 x 2
12T88	$C_2^4:A_4$	$192$	$-1$	✓	$-1$	$20$	$C_3$, $A_4$	12T87 x 2, 12T88, 16T416 x 2, 24T441 x 2, 24T442 x 2, 24T443 x 4, 24T444 x 2, 24T445 x 2, 24T446 x 2, 24T447 x 2, 24T448 x 4, 24T449, 24T450, 24T451 x 4, 24T452 x 4, 32T2183 x 2
12T89	$C_2^4.A_4$	$192$	$1$	✓	$-1$	$20$	$C_3$, $A_4\times C_2$	12T89, 12T92 x 2, 24T453 x 2, 24T454 x 2, 24T455 x 4, 24T456 x 4, 24T463, 24T464, 24T465 x 4, 24T466 x 4, 32T2188 x 2
12T90	$C_2^2\wr C_3$	$192$	$1$	✓	$-1$	$32$	$C_3$, $A_4\times C_2$ x 3	12T90 x 59, 24T457 x 90, 24T458 x 90, 24T459 x 120
12T91	$C_2^3.\SL(2,3)$	$192$	$1$	✓	$-1$	$18$	$C_3$, $A_4\times C_2$	12T91, 12T93 x 2, 24T460, 24T461 x 2, 24T462, 24T467, 24T468, 32T2187 x 2
12T92	$C_2^4.A_4$	$192$	$-1$	✓	$-1$	$20$	$C_3$, $A_4$	12T89 x 2, 12T92, 24T453 x 2, 24T454 x 2, 24T455 x 4, 24T456 x 4, 24T463, 24T464, 24T465 x 4, 24T466 x 4, 32T2188 x 2
12T93	$C_2^3.\SL(2,3)$	$192$	$-1$	✓	$-1$	$18$	$C_3$, $A_4$	12T91 x 2, 12T93, 24T460, 24T461 x 2, 24T462, 24T467, 24T468, 32T2187 x 2
12T94	$C_4\wr C_3$	$192$	$-1$	✓	$-1$	$32$	$C_3$, $A_4\times C_2$	12T94 x 3, 24T469 x 4, 24T470 x 2
12T95	$C_4^2:D_6$	$192$	$1$	✓	$-1$	$20$	$S_3$, $S_4$	12T95, 12T96, 12T97, 24T471, 24T472 x 2, 24T473 x 2, 24T474 x 2, 24T475 x 2, 24T476, 24T477, 24T478, 24T479 x 2, 24T480 x 2, 32T2216 x 2
12T96	$C_4^2:D_6$	$192$	$-1$	✓	$-1$	$20$	$S_3$, $S_4$	12T95 x 2, 12T97, 24T471, 24T472 x 2, 24T473 x 2, 24T474 x 2, 24T475 x 2, 24T476, 24T477, 24T478, 24T479 x 2, 24T480 x 2, 32T2216 x 2
12T97	$C_4^2:D_6$	$192$	$1$	✓	$-1$	$20$	$S_3$, $S_4$	12T95 x 2, 12T96, 24T471, 24T472 x 2, 24T473 x 2, 24T474 x 2, 24T475 x 2, 24T476, 24T477, 24T478, 24T479 x 2, 24T480 x 2, 32T2216 x 2
12T98	$C_2^3.S_4$	$192$	$-1$	✓	$-1$	$20$	$S_3$, $S_4$	12T98, 24T317, 24T481, 24T482 x 2
12T99	$C_2^4:C_{12}$	$192$	$-1$	✓	$-1$	$20$	$C_3$, $A_4\times C_2$	12T99, 12T105 x 2, 16T418 x 2, 24T483 x 2, 24T484 x 2, 24T501 x 2, 24T502 x 4, 24T503 x 2, 24T504 x 2, 24T505 x 2, 24T506 x 2, 24T507 x 4
12T100	$C_2^3:S_4$	$192$	$-1$	✓	$-1$	$20$	$S_3$, $S_4$	12T100 x 2, 12T101 x 6, 12T103 x 6, 12T106, 16T429, 24T432 x 3, 24T485 x 3, 24T486 x 6, 24T487 x 6, 24T488 x 3, 24T489 x 3, 24T490 x 3, 24T491 x 2, 24T492 x 6, 24T493 x 6, 24T508 x 3, 24T509 x 6, 24T510, 24T511, 32T2212 x 2
12T101	$C_2^3:S_4$	$192$	$1$	✓	$-1$	$20$	$S_3$, $S_4$, $S_4\times C_2$ x 2	12T100 x 3, 12T101 x 5, 12T103 x 6, 12T106, 16T429, 24T432 x 3, 24T485 x 3, 24T486 x 6, 24T487 x 6, 24T488 x 3, 24T489 x 3, 24T490 x 3, 24T491 x 2, 24T492 x 6, 24T493 x 6, 24T508 x 3, 24T509 x 6, 24T510, 24T511, 32T2212 x 2
12T102	$C_2^3.S_4$	$192$	$-1$	✓	$-1$	$20$	$S_3$, $S_4$	12T102 x 2, 12T107, 16T434, 24T386 x 3, 24T433 x 3, 24T494 x 3, 24T495 x 6, 24T512 x 3, 24T513 x 6, 24T514, 24T515
12T103	$C_2^3:S_4$	$192$	$1$	✓	$-1$	$20$	$S_3$, $S_4$, $S_4\times C_2$ x 2	12T100 x 3, 12T101 x 6, 12T103 x 5, 12T106, 16T429, 24T432 x 3, 24T485 x 3, 24T486 x 6, 24T487 x 6, 24T488 x 3, 24T489 x 3, 24T490 x 3, 24T491 x 2, 24T492 x 6, 24T493 x 6, 24T508 x 3, 24T509 x 6, 24T510, 24T511, 32T2212 x 2
12T104	$C_2^3.(C_2\times A_4)$	$192$	$-1$	✓	$-1$	$18$	$C_3$, $A_4\times C_2$	12T104 x 3, 24T496 x 2, 24T497 x 2, 24T498 x 2, 24T499 x 4, 24T500 x 4

 

Results are complete for degrees $\leq 23$.