Galois group search results

Results (18 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
14T14	$C_7:F_7$	$294$	$-1$	✓	$-1$	$17$	$C_2$	14T14 x 2, 42T61 x 3
14T15	$C_7^2:S_3$	$294$	$-1$	✓	$-1$	$20$	$C_2$	21T17, 21T18, 42T56, 42T57, 42T62
14T16	$\PGL(2,7)$	$336$	$-1$		$-1$	$9$	$C_2$	8T43, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
14T17	$C_2\times \GL(3,2)$	$336$	$-1$		$-1$	$12$	$\GL(3,2)$	14T17, 14T19 x 2, 16T714, 28T43 x 2, 42T78, 42T79, 42T80 x 2
14T18	$F_8:C_6$	$336$	$-1$	✓	$-1$	$16$	$C_7:C_3$	16T712, 28T44, 42T67
14T19	$\GL(3,2) \times C_2$	$336$	$-1$		$-1$	$12$	$C_2$, $\GL(3,2)$	14T17 x 2, 14T19, 16T714, 28T43 x 2, 42T78, 42T79, 42T80 x 2
14T20	$D_7 \wr C_2$	$392$	$-1$	✓	$-1$	$20$	$C_2$	14T20, 28T53 x 2, 28T54 x 2, 28T55 x 2, 28T57
14T21	$C_2^3:F_8$	$448$	$1$	✓	$-1$	$16$	$C_7$	14T21 x 6, 28T62 x 21, 28T63 x 14, 28T64 x 42, 28T65 x 7, 28T66 x 7
15T17	$(C_5^2 : C_3):C_4$	$300$	$1$	✓	$-1$	$8$	$S_3$	15T17, 25T28, 30T71 x 2
15T18	$((C_5^2 : C_3):C_2):C_2$	$300$	$-1$	✓	$-1$	$14$	$S_3$	15T18, 25T27, 30T66 x 2, 30T72 x 2, 30T80 x 2
15T19	$(C_5^2 : C_4):C_3$	$300$	$-1$	✓	$-1$	$14$	$C_3$	15T19, 25T26, 30T78 x 2
15T20	$A_6$	$360$	$1$		$-1$	$7$		6T15 x 2, 10T26, 15T20, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
15T21	$\GL(2,4):C_2$	$360$	$1$		$-1$	$12$	$S_5$	15T21, 15T22, 18T146, 30T89, 30T93 x 2, 30T101, 36T554, 45T45
15T22	$\GL(2,4):C_2$	$360$	$1$		$-1$	$12$	$S_3$, $S_5$	15T21 x 2, 18T146, 30T89, 30T93 x 2, 30T101, 36T554, 45T45
15T23	$A_5 \times S_3$	$360$	$-1$		$-1$	$15$	$S_3$, $A_5$	18T145, 30T85, 30T94, 30T102, 36T551, 36T552, 36T553, 45T40
15T24	$S_5 \times C_3$	$360$	$-1$		$-1$	$21$	$C_3$, $S_5$	18T144, 30T90, 30T98, 30T103, 36T550, 45T44
15T25	$C_5\wr C_3$	$375$	$1$	✓	$-1$	$55$	$C_3$	15T25 x 7
15T26	$C_3^4:C_5$	$405$	$1$	✓	$-1$	$21$	$C_5$	15T26 x 7, 45T61 x 2, 45T62 x 16, 45T63 x 8

 

Results are complete for degrees $\leq 23$.