Galois group search results

Results (1-50 of 10197 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
25T1	$C_{25}$	$25$	$1$	✓	$1$	$25$	$C_5$
25T2	$C_5^2$	$25$	$1$	✓	$1$	$25$	$C_5$ x 6
25T3	$C_5\times D_5$	$50$	$1$	✓	$-1$	$20$	$C_5$, $D_{5}$	10T6 x 2
25T4	$D_{25}$	$50$	$1$	✓	$-1$	$14$	$D_{5}$
25T5	$C_5:D_5$	$50$	$1$	✓	$-1$	$14$	$D_{5}$ x 6
25T7	$C_5\times F_5$	$100$	$-1$	✓	$-1$	$25$	$C_5$, $F_5$	20T29
25T8	$C_{25}:C_4$	$100$	$1$	✓	$-1$	$10$	$F_5$
25T9	$C_5:F_5$	$100$	$1$	✓	$-1$	$10$	$F_5$ x 6
25T10	$C_5:F_5$	$100$	$1$	✓	$-1$	$10$	$F_5$ x 2	10T10 x 2, 20T27 x 2
25T11	$C_5:F_5$	$100$	$-1$	✓	$-1$	$13$	$D_{5}$, $F_5$	20T26
25T12	$D_5^2$	$100$	$1$	✓	$-1$	$16$	$D_{5}$ x 2	10T9 x 2, 20T28 x 2
25T13	$C_{25}:C_5$	$125$	$1$	✓	$2$	$29$	$C_5$
25T14	$\He_5$	$125$	$1$	✓	$2$	$29$	$C_5$	25T14 x 5
25T18	$D_5\times F_5$	$200$	$-1$	✓	$-1$	$20$	$D_{5}$, $F_5$	20T51, 40T168
25T19	$D_5:F_5$	$200$	$1$	✓	$-1$	$14$	$F_5$ x 2	10T17 x 2, 20T54 x 2, 40T169 x 2
25T22	$C_5^2:D_5$	$250$	$1$	✓	$-1$	$22$	$D_{5}$	25T22 x 5
25T23	$C_5^2:C_{10}$	$250$	$1$	✓	$-1$	$22$	$D_{5}$	25T24
25T24	$C_5^2:C_{10}$	$250$	$1$	✓	$-1$	$22$	$C_5$	25T23
25T25	$C_{25}:C_{10}$	$250$	$1$	✓	$-1$	$22$	$D_{5}$
25T29	$C_5\times A_5$	$300$	$1$		$-1$	$25$	$C_5$, $A_5$	30T69
25T32	$F_5^2$	$400$	$-1$	✓	$-1$	$25$	$F_5$ x 2	20T102, 40T396
25T33	$C_5^2:F_5$	$500$	$-1$	✓	$-1$	$14$	$F_5$	25T33 x 5
25T34	$C_5^2:C_{20}$	$500$	$1$	✓	$-1$	$26$	$F_5$	25T37
25T35	$C_5^2:F_5$	$500$	$-1$	✓	$-1$	$26$	$F_5$	25T35
25T36	$C_5^2:F_5$	$500$	$-1$	✓	$-1$	$14$	$D_{5}$	25T39
25T37	$C_5^2:C_{20}$	$500$	$-1$	✓	$-1$	$26$	$C_5$	25T34
25T38	$C_5^2:D_{10}$	$500$	$1$	✓	$-1$	$20$	$D_{5}$	25T38
25T39	$C_5^2:F_5$	$500$	$1$	✓	$-1$	$14$	$F_5$	25T36
25T40	$C_{25}:C_{20}$	$500$	$1$	✓	$-1$	$26$	$F_5$
25T42	$C_5\times S_5$	$600$	$-1$		$-1$	$35$	$C_5$, $S_5$	30T145
25T44	$C_5:S_5$	$600$	$-1$		$-1$	$17$	$D_{5}$, $S_5$	30T144
25T46	$D_5\times A_5$	$600$	$1$		$-1$	$20$	$D_{5}$, $A_5$	30T128
25T48	$C_5^3:C_5$	$625$	$1$	✓	$3$	$49$	$C_5$	25T48 x 4
25T49	$C_5^3.C_5$	$625$	$1$	✓	$3$	$49$	$C_5$	25T49 x 4
25T51	$C_5^2:(C_2\times F_5)$	$1000$	$-1$	✓	$-1$	$22$	$F_5$	25T51
25T52	$C_5^2:(C_4\times D_5)$	$1000$	$1$	✓	$-1$	$22$	$F_5$	25T53
25T53	$C_5^2:(C_4\times D_5)$	$1000$	$-1$	✓	$-1$	$22$	$D_{5}$	25T52
25T54	$F_5\times A_5$	$1200$	$-1$		$-1$	$25$	$F_5$, $A_5$	30T245
25T55	$A_5:F_5$	$1200$	$1$		$-1$	$19$	$F_5$, $S_5$	30T250
25T58	$D_5\times S_5$	$1200$	$-1$		$-1$	$28$	$D_{5}$, $S_5$	30T252
25T59	$C_5^3:C_{10}$	$1250$	$1$	✓	$-1$	$32$	$C_5$	25T59 x 4
25T60	$C_5^3:D_5$	$1250$	$1$	✓	$-1$	$62$	$D_{5}$	25T60 x 4
25T61	$C_5^3.D_5$	$1250$	$1$	✓	$-1$	$32$	$D_{5}$	25T61 x 4
25T62	$C_5^3:D_5$	$1250$	$1$	✓	$-1$	$32$	$D_{5}$	25T62 x 4
25T63	$\He_5:C_4^2$	$2000$	$-1$	✓	$-1$	$29$	$F_5$	25T63
25T64	$F_5\times S_5$	$2400$	$-1$		$-1$	$35$	$F_5$, $S_5$	30T380
25T66	$C_5^3.F_5$	$2500$	$1$	✓	$-1$	$31$	$F_5$
25T67	$C_5^3:C_{20}$	$2500$	$-1$	✓	$-1$	$31$	$C_5$	25T67 x 4
25T68	$C_5^3:D_{10}$	$2500$	$1$	✓	$-1$	$40$	$D_{5}$	25T68 x 4
25T69	$\He_5:C_{20}$	$2500$	$-1$	✓	$-1$	$46$	$F_5$

 

Results are complete for degrees $\leq 23$.