Galois group search results

Results (1-50 of 407 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
35T1	$C_{35}$	$35$	$1$	✓	$1$	$35$	$C_5$, $C_7$
35T2	$C_7\times D_5$	$70$	$1$	✓	$-1$	$28$	$D_{5}$, $C_7$
35T3	$C_5\times D_7$	$70$	$-1$	✓	$-1$	$25$	$C_5$, $D_{7}$
35T4	$D_{35}$	$70$	$-1$	✓	$-1$	$19$	$D_{5}$, $D_{7}$
35T5	$C_7:C_{15}$	$105$	$1$	✓	$-1$	$25$	$C_5$, $C_7:C_3$
35T6	$C_7\times F_5$	$140$	$-1$	✓	$-1$	$35$	$F_5$, $C_7$
35T7	$D_5\times D_7$	$140$	$-1$	✓	$-1$	$20$	$D_{5}$, $D_{7}$
35T8	$C_{35}:C_4$	$140$	$1$	✓	$-1$	$17$	$F_5$, $D_{7}$
35T9	$C_{35}:C_6$	$210$	$1$	✓	$-1$	$20$	$D_{5}$, $C_7:C_3$
35T10	$C_5\times F_7$	$210$	$-1$	✓	$-1$	$35$	$C_5$, $F_7$
35T11	$C_{35}:C_6$	$210$	$-1$	✓	$-1$	$17$	$D_{5}$, $F_7$
35T12	$D_7\times F_5$	$280$	$-1$	✓	$-1$	$25$	$F_5$, $D_{7}$
35T13	$C_7\times A_5$	$420$	$1$		$-1$	$35$	$A_5$, $C_7$	42T86
35T14	$C_{35}:C_{12}$	$420$	$-1$	✓	$-1$	$25$	$F_5$, $C_7:C_3$
35T15	$D_5\times F_7$	$420$	$-1$	✓	$-1$	$28$	$D_{5}$, $F_7$
35T16	$C_{35}:C_{12}$	$420$	$1$	✓	$-1$	$19$	$F_5$, $F_7$
35T17	$C_7\times S_5$	$840$	$-1$		$-1$	$49$	$S_5$, $C_7$	42T138
35T18	$D_7\times A_5$	$840$	$-1$		$-1$	$25$	$A_5$, $D_{7}$	42T139
35T19	$C_7:S_5$	$840$	$1$		$-1$	$22$	$S_5$, $D_{7}$	42T140
35T20	$F_5\times F_7$	$840$	$-1$	✓	$-1$	$35$	$F_5$, $F_7$
35T21	$C_5\times \GL(3,2)$	$840$	$1$		$-1$	$30$	$C_5$, $\GL(3,2)$	35T21, 40T885
35T22	$C_7:\GL(2,4)$	$1260$	$1$		$-1$	$25$	$A_5$, $C_7:C_3$	42T197
35T23	$D_7\times S_5$	$1680$	$-1$		$-1$	$35$	$S_5$, $D_{7}$	42T218
35T24	$D_5\times \GL(3,2)$	$1680$	$1$		$-1$	$24$	$D_{5}$, $\GL(3,2)$	35T24, 40T1570
35T25	$C_7:C_3\times S_5$	$2520$	$-1$		$-1$	$35$	$S_5$, $C_7:C_3$	42T296
35T26	$A_5:F_7$	$2520$	$1$		$-1$	$26$	$S_5$, $F_7$	42T298
35T27	$F_7\times A_5$	$2520$	$-1$		$-1$	$35$	$A_5$, $F_7$	42T297
35T28	$A_7$	$2520$	$1$		$-1$	$9$		7T6, 15T47 x 2, 21T33, 42T294, 42T299
35T29	$F_5\times \GL(3,2)$	$3360$	$-1$		$-1$	$30$	$F_5$, $\GL(3,2)$	35T29, 40T2719
35T30	$F_7\times S_5$	$5040$	$-1$		$-1$	$49$	$S_5$, $F_7$	42T417
35T31	$S_7$	$5040$	$1$		$-1$	$15$		7T7, 14T46, 21T38, 30T565, 42T411, 42T412, 42T413, 42T418
35T32	$A_5\times \GL(3,2)$	$10080$	$1$		$-1$	$30$	$A_5$, $\GL(3,2)$	35T32, 40T5863, 42T552 x 2
35T33	$C_7^4:C_5$	$12005$	$1$	✓	$-1$	$485$	$C_5$	35T33 x 79
35T34	$C_5\times A_7$	$12600$	$1$		$-1$	$45$	$C_5$, $A_7$
35T35	$S_5\times \GL(3,2)$	$20160$	$-1$		$-1$	$42$	$S_5$, $\GL(3,2)$	35T35, 40T11250, 42T723 x 2
35T36	$A_8$	$20160$	$1$		$-1$	$14$		8T49, 15T72 x 2, 28T433
35T37	$C_7^4:C_{10}$	$24010$	$-1$	✓	$-1$	$250$	$C_5$	35T37 x 79
35T38	$C_7^4:D_5$	$24010$	$1$	✓	$-1$	$316$	$D_{5}$	35T38 x 7, 35T39 x 8
35T39	$C_7^4:D_5$	$24010$	$-1$	✓	$-1$	$316$	$D_{5}$	35T38 x 8, 35T39 x 7
35T40	$D_5\times A_7$	$25200$	$1$		$-1$	$36$	$D_{5}$, $A_7$
35T41	$C_5\times S_7$	$25200$	$-1$		$-1$	$75$	$C_5$, $S_7$
35T42	$C_5:S_7$	$25200$	$-1$		$-1$	$33$	$D_{5}$, $S_7$
35T43	$C_7^4:C_{15}$	$36015$	$1$	✓	$-1$	$175$	$C_5$	35T43 x 79
35T44	$S_8$	$40320$	$1$		$-1$	$22$		8T50, 16T1838, 28T502, 30T1153
35T45	$C_7^4:D_{10}$	$48020$	$-1$	✓	$-1$	$200$	$D_{5}$	35T45 x 15
35T46	$C_7^4:F_5$	$48020$	$-1$	✓	$-1$	$179$	$F_5$	35T47
35T47	$C_7^4:F_5$	$48020$	$1$	✓	$-1$	$179$	$F_5$	35T46
35T48	$F_5\times A_7$	$50400$	$-1$		$-1$	$45$	$F_5$, $A_7$
35T49	$D_5\times S_7$	$50400$	$-1$		$-1$	$60$	$D_{5}$, $S_7$
35T50	$A_7:F_5$	$50400$	$1$		$-1$	$39$	$F_5$, $S_7$

 

Results are complete for degrees $\leq 23$.