Galois group search results

Results (1-50 of 1854 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
28T1	$C_{28}$	$28$	$-1$	✓	$1$	$28$	$C_2$, $C_4$, $C_7$, $C_{14}$
28T2	$C_2\times C_{14}$	$28$	$1$	✓	$1$	$28$	$C_2$ x 3, $C_2^2$, $C_7$, $C_{14}$ x 3
28T3	$C_7:C_4$	$28$	$-1$	✓	$-1$	$10$	$C_2$, $C_4$, $D_{7}$, $D_{7}$
28T4	$D_{14}$	$28$	$1$	✓	$-1$	$10$	$C_2$ x 3, $C_2^2$, $D_{7}$, $D_{7}$, $D_{14}$ x 2	14T3 x 2
28T5	$C_7\times D_4$	$56$	$-1$	✓	$2$	$35$	$C_2$, $D_{4}$, $C_7$, $C_{14}$	28T5
28T6	$D_{14}:C_2$	$56$	$-1$	✓	$-1$	$17$	$C_2$, $D_{4}$, $D_{7}$, $D_{7}$	28T7
28T7	$D_{14}:C_2$	$56$	$-1$	✓	$-1$	$17$	$C_2$, $D_{4}$, $D_{7}$, $D_{14}$	28T6
28T8	$C_4\times D_7$	$56$	$-1$	✓	$-1$	$20$	$C_2$, $C_4$, $D_{7}$, $D_{14}$	28T8
28T9	$C_2^2\times D_7$	$56$	$1$	✓	$-1$	$20$	$C_2$ x 3, $C_2^2$, $D_{7}$, $D_{14}$ x 3	28T9 x 3
28T10	$D_{28}$	$56$	$-1$	✓	$-1$	$17$	$C_2$, $D_{4}$, $D_{7}$, $D_{14}$	28T10
28T11	$F_8$	$56$	$1$	✓	$-1$	$8$	$C_7$, $F_8$	8T25, 14T6
28T12	$C_7:C_{12}$	$84$	$-1$	✓	$-1$	$14$	$C_2$, $C_4$, $F_7$, $F_7$
28T13	$C_4\times C_7:C_3$	$84$	$-1$	✓	$-1$	$20$	$C_2$, $C_4$, $C_7:C_3$, $(C_7:C_3) \times C_2$
28T14	$C_2^2\times C_7:C_3$	$84$	$1$	✓	$-1$	$20$	$C_2$ x 3, $C_2^2$, $C_7:C_3$, $(C_7:C_3) \times C_2$ x 3
28T15	$C_2\times F_7$	$84$	$1$	✓	$-1$	$14$	$C_2$ x 3, $C_2^2$, $F_7$, $F_7$, $F_7 \times C_2$ x 2	14T7 x 2, 42T10 x 2
28T16	$C_7:A_4$	$84$	$1$	✓	$-1$	$12$	$A_4$, $C_7:C_3$	42T8
28T17	$C_7\times A_4$	$84$	$1$	✓	$-1$	$28$	$A_4$, $C_7$	42T7
28T18	$D_4\times D_7$	$112$	$-1$	✓	$-1$	$25$	$C_2$, $D_{4}$, $D_{7}$, $D_{14}$	28T18 x 3
28T19	$C_2\times F_8$	$112$	$1$	✓	$-1$	$16$	$C_7$, $F_8$, $C_2\times F_8$	14T9, 16T196, 28T19 x 2, 28T20
28T20	$C_2\times F_8$	$112$	$1$	✓	$-1$	$16$	$C_2$, $C_7$, $C_{14}$, $F_8$, $C_2\times F_8$	14T9, 16T196, 28T19 x 3
28T21	$C_2^2:F_7$	$168$	$-1$	✓	$-1$	$19$	$C_2$, $D_{4}$, $F_7$, $F_7$	28T25
28T22	$D_4\times C_7:C_3$	$168$	$-1$	✓	$-1$	$25$	$C_2$, $D_{4}$, $C_7:C_3$, $(C_7:C_3) \times C_2$	28T22
28T23	$D_{28}:C_3$	$168$	$-1$	✓	$-1$	$19$	$C_2$, $D_{4}$, $F_7$, $F_7 \times C_2$	28T23
28T24	$C_2^2\times F_7$	$168$	$1$	✓	$-1$	$28$	$C_2$ x 3, $C_2^2$, $F_7$, $F_7 \times C_2$ x 3	28T24 x 3
28T25	$C_2^2:F_7$	$168$	$-1$	✓	$-1$	$19$	$C_2$, $D_{4}$, $F_7$, $F_7 \times C_2$	28T21
28T26	$C_4\times F_7$	$168$	$-1$	✓	$-1$	$28$	$C_2$, $C_4$, $F_7$, $F_7 \times C_2$	28T26
28T27	$F_8:C_3$	$168$	$1$	✓	$-1$	$8$	$C_7:C_3$	8T36, 14T11, 24T283, 42T26
28T28	$D_7:A_4$	$168$	$1$	✓	$-1$	$12$	$A_4$, $F_7$	42T30, 42T31
28T29	$A_4\times D_7$	$168$	$1$	✓	$-1$	$20$	$A_4$, $D_{7}$	42T28, 42T29
28T30	$C_7:S_4$	$168$	$-1$	✓	$-1$	$17$	$S_4$, $D_{7}$	42T32, 42T33
28T31	$C_7\times S_4$	$168$	$-1$	✓	$-1$	$35$	$S_4$, $C_7$	42T34, 42T35
28T32	$\PSL(2,7)$	$168$	$1$		$-1$	$6$	$\GL(3,2)$ x 2	7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 42T37, 42T38 x 2
28T33	$C_7\times C_7:C_4$	$196$	$-1$	✓	$-1$	$70$	$C_2$, $C_4$, $C_7 \wr C_2$	28T33 x 2
28T34	$C_{14}\times D_7$	$196$	$1$	✓	$-1$	$70$	$C_2$ x 3, $C_2^2$, $C_7 \wr C_2$	28T34 x 2
28T35	$C_7:D_7.C_2$	$196$	$-1$	✓	$-1$	$16$	$C_2$, $C_4$, $C_7:D_7.C_2$	14T12 x 4, 28T35 x 3
28T36	$D_7^2$	$196$	$1$	✓	$-1$	$25$	$C_2$ x 3, $C_2^2$, $D_7^2$	14T13 x 3, 28T36 x 2
28T37	$C_4\times F_8$	$224$	$-1$	✓	$-1$	$32$	$C_2$, $C_7$, $C_{14}$	32T2229
28T38	$C_2^2\times F_8$	$224$	$1$	✓	$-1$	$32$	$C_7$, $C_2\times F_8$ x 3	28T38 x 5, 28T39 x 3, 32T2228
28T39	$C_2^2\times F_8$	$224$	$1$	✓	$-1$	$32$	$C_2$, $C_7$, $C_{14}$, $C_2\times F_8$ x 2	28T38 x 6, 28T39 x 2, 32T2228
28T40	$A_4\times C_7:C_3$	$252$	$1$	✓	$-1$	$20$	$A_4$, $C_7:C_3$	42T39
28T41	$D_4\times F_7$	$336$	$-1$	✓	$-1$	$35$	$C_2$, $D_{4}$, $F_7$, $F_7 \times C_2$	28T41 x 3
28T42	$\SO(3,7)$	$336$	$1$		$-1$	$9$	$C_2$, $\SO(3,7)$	8T43, 14T16, 16T713, 21T20, 24T707, 28T46, 42T81, 42T82, 42T83
28T43	$C_2\times \PSL(2,7)$	$336$	$1$		$-1$	$12$	$C_2$, $\GL(3,2)$, $\PSL(2,7)$, $C_2\times \PSL(2,7)$, $\GL(3,2) \times C_2$	14T17 x 2, 14T19 x 2, 16T714, 28T43, 42T78, 42T79, 42T80 x 2
28T44	$C_2\times F_8:C_3$	$336$	$1$	✓	$-1$	$16$	$C_2$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $F_8:C_3$, $C_2\times F_8:C_3$	14T18, 16T712, 42T67
28T45	$D_7\times S_4$	$336$	$-1$	✓	$-1$	$25$	$S_4$, $D_{7}$	42T74, 42T75, 42T76, 42T77
28T46	$\SO(3,7)$	$336$	$1$		$-1$	$9$		8T43, 14T16, 16T713, 21T20, 24T707, 28T42, 42T81, 42T82, 42T83
28T47	$C_7\times D_{14}:C_2$	$392$	$-1$	✓	$-1$	$119$	$C_2$, $D_{4}$, $C_7 \wr C_2$	28T47 x 5
28T48	$C_2\times C_7:D_7.C_2$	$392$	$1$	✓	$-1$	$32$	$C_2$ x 3, $C_2^2$, $C_7:D_7.C_2$	28T48 x 3, 28T49 x 4
28T49	$C_2\times C_7:D_7.C_2$	$392$	$-1$	✓	$-1$	$32$	$C_2$, $C_4$, $C_7:D_7.C_2$	28T48 x 4, 28T49 x 3
28T50	$(C_{14}\times D_7):C_2$	$392$	$-1$	✓	$-1$	$47$	$C_2$, $D_{4}$, $D_7^2$	28T50 x 5

 

Results are complete for degrees $\leq 23$.