Galois group search results

Results (1-50 of 63 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
14T1	$C_{14}$	$14$	$-1$	✓	$1$	$14$	$C_2$, $C_7$
14T2	$D_{7}$	$14$	$-1$	✓	$-1$	$5$	$C_2$, $D_{7}$	7T2
14T3	$D_{14}$	$28$	$-1$	✓	$-1$	$10$	$C_2$, $D_{7}$	14T3, 28T4
14T4	$F_7$	$42$	$-1$	✓	$-1$	$7$	$C_2$, $F_7$	7T4, 21T4, 42T4
14T5	$(C_7:C_3) \times C_2$	$42$	$-1$	✓	$-1$	$10$	$C_2$, $C_7:C_3$	42T2
14T6	$F_8$	$56$	$1$	✓	$-1$	$8$	$C_7$	8T25, 28T11
14T7	$F_7 \times C_2$	$84$	$-1$	✓	$-1$	$14$	$C_2$, $F_7$	14T7, 28T15, 42T10 x 2
14T8	$C_7 \wr C_2$	$98$	$-1$	✓	$-1$	$35$	$C_2$	14T8 x 2
14T9	$C_2\times F_8$	$112$	$-1$	✓	$-1$	$16$	$C_7$	16T196, 28T19 x 3, 28T20
14T10	$\PSL(2,7)$	$168$	$1$		$-1$	$6$	$\GL(3,2)$	7T5 x 2, 8T37, 14T10, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
14T11	$F_8:C_3$	$168$	$1$	✓	$-1$	$8$	$C_7:C_3$	8T36, 24T283, 28T27, 42T26
14T12	$C_7:D_7.C_2$	$196$	$1$	✓	$-1$	$16$	$C_2$	14T12 x 3, 28T35 x 4
14T13	$D_7^2$	$196$	$-1$	✓	$-1$	$25$	$C_2$	14T13 x 2, 28T36 x 3
14T14	$C_7^2:C_6$	$294$	$-1$	✓	$-1$	$17$	$C_2$	14T14 x 2, 42T61 x 3
14T15	$C_7^2:S_3$	$294$	$-1$	✓	$-1$	$20$	$C_2$	21T17, 21T18, 42T56, 42T57, 42T62
14T16	$\SO(3,7)$	$336$	$-1$		$-1$	$9$	$C_2$	8T43, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
14T17	$C_2\times \PSL(2,7)$	$336$	$-1$		$-1$	$12$	$\GL(3,2)$	14T17, 14T19 x 2, 16T714, 28T43 x 2, 42T78, 42T79, 42T80 x 2
14T18	$C_2\times F_8:C_3$	$336$	$-1$	✓	$-1$	$16$	$C_7:C_3$	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
14T22	$C_7^2:(C_3:C_4)$	$588$	$1$	✓	$-1$	$10$	$C_2$	28T75, 42T119, 42T125
14T23	$C_7^2:C_{12}$	$588$	$1$	✓	$-1$	$16$	$C_2$	14T23 x 3, 28T76 x 4, 42T120 x 4
14T24	$C_7^2:(C_2\times C_6)$	$588$	$-1$	✓	$-1$	$19$	$C_2$	14T24 x 2, 28T77 x 3, 42T121 x 3
14T25	$C_7^2:D_6$	$588$	$-1$	✓	$-1$	$19$	$C_2$	21T23 x 2, 28T78, 42T110 x 2, 42T111 x 2, 42T112 x 2, 42T122
14T26	$C_7^2:(C_3\times S_3)$	$882$	$-1$	✓	$-1$	$20$	$C_2$	21T25, 21T26, 42T143, 42T144, 42T152, 42T153, 42T154, 42T155
14T27	2^7[1/2]D(7)	$896$	$-1$	✓	$-1$	$20$	$D_{7}$	14T27 x 6, 14T28 x 7, 16T1078, 28T98, 28T105 x 7, 28T106 x 21, 28T107 x 21, 28T108 x 7, 28T109 x 7
14T28	[2^6]D(7)	$896$	$1$	✓	$-1$	$20$	$D_{7}$	14T27 x 7, 14T28 x 6, 16T1078, 28T98, 28T105 x 7, 28T106 x 21, 28T107 x 21, 28T108 x 7, 28T109 x 7
14T29	$C_2 \wr C_7$	$896$	$-1$	✓	$-1$	$32$	$C_7$	14T29 x 6, 28T104 x 7, 28T110 x 21, 28T111 x 42, 28T112 x 42, 28T113 x 21, 28T114 x 42, 28T115 x 42, 28T116 x 14, 28T117 x 42, 28T118 x 7
14T30	$\PSL(2,13)$	$1092$	$1$		$-1$	$9$		28T120, 42T176
14T31	$C_7^2:(C_3:D_4)$	$1176$	$-1$	✓	$-1$	$17$	$C_2$	28T133, 28T134, 28T135, 42T194, 42T196
14T32	$C_7^2:(C_3\times D_4)$	$1176$	$-1$	✓	$-1$	$20$	$C_2$	14T32, 28T136 x 2, 28T137 x 2, 28T138 x 2, 28T143, 42T195 x 2
14T33	$C_2^3.\PSL(2,7)$	$1344$	$1$		$-1$	$11$	$\GL(3,2)$	14T33, 28T152, 28T158 x 2, 42T208 x 2, 42T209 x 2
14T34	$C_2^3.\PSL(2,7)$	$1344$	$1$		$-1$	$11$	$\GL(3,2)$	8T48 x 2, 14T34, 28T153, 28T159 x 2, 42T210 x 2, 42T211 x 2
14T35	$C_2^3:F_8.C_3$	$1344$	$1$	✓	$-1$	$16$	$C_7:C_3$	28T154, 28T155 x 2, 28T157, 42T202, 42T204, 42T205
14T36	$C_7^2:(C_3\times C_3:C_4)$	$1764$	$1$	✓	$-1$	$22$	$C_2$	28T169, 42T248, 42T249, 42T250, 42T251, 42T257
14T37	$C_7^2:(C_6\times S_3)$	$1764$	$-1$	✓	$-1$	$25$	$C_2$	21T29 x 2, 28T170, 42T223 x 2, 42T224 x 2, 42T225 x 2, 42T252, 42T253, 42T254, 42T255
14T38	[2^7]D(7)=2wrD(7)	$1792$	$-1$	✓	$-1$	$40$	$D_{7}$	14T38 x 13, 28T175, 28T185 x 21, 28T186 x 7, 28T193 x 7, 28T194 x 42, 28T195 x 42, 28T196 x 14, 28T197 x 14, 32T97728
14T39	$\PGL(2,13)$	$2184$	$-1$		$-1$	$15$		28T201, 42T284
14T40	1/2[2^7]F_42(7)	$2688$	$-1$	✓	$-1$	$20$	$F_7$	14T41, 16T1502, 28T215, 28T227, 28T228, 28T237, 42T314, 42T315, 42T316, 42T317, 42T318, 42T319
14T41	[2^6]F_42(7)	$2688$	$1$	✓	$-1$	$20$	$F_7$	14T40, 16T1502, 28T215, 28T227, 28T228, 28T237, 42T314, 42T315, 42T316, 42T317, 42T318, 42T319
14T42	2^4`L_7(14)	$2688$	$-1$		$-1$	$22$	$\GL(3,2)$	14T42, 28T229 x 2, 28T230, 28T231 x 2, 42T327 x 2, 42T330 x 2
14T43	2^4:L_7(14)=[2^4]L(7)	$2688$	$-1$		$-1$	$22$	$\GL(3,2)$	14T43, 16T1504 x 2, 28T232 x 2, 28T233, 28T234 x 2, 42T328 x 2, 42T329 x 2
14T44	[2^7]F_21(7)=2wrF_21(7)	$2688$	$-1$	✓	$-1$	$32$	$C_7:C_3$	28T226, 28T235 x 2, 28T236, 42T309, 42T310, 42T311
14T45	[F_42(7)^2]2=F_42(7)wr2	$3528$	$-1$	✓	$-1$	$35$	$C_2$	28T251, 28T252, 28T253, 42T368, 42T369, 42T370, 42T371, 42T372
14T46	2[1/2]S(7)	$5040$	$-1$		$-1$	$15$	$C_2$, $S_7$	7T7, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
14T47	$A_7\times C_2$	$5040$	$-1$		$-1$	$18$	$C_2$, $A_7$	30T566 x 2, 42T409, 42T410
14T48	[2^7]F_42(7)=2wrF_42(7)	$5376$	$-1$	✓	$-1$	$40$	$F_7$	14T48, 28T287, 28T308, 28T315, 28T316 x 2, 28T317 x 2, 32T397084, 42T448 x 2, 42T449 x 2, 42T450 x 2
14T49	$S_7\times C_2$	$10080$	$-1$		$-1$	$30$	$C_2$, $S_7$	14T49, 28T363, 42T549 x 2, 42T550 x 2
14T50	[2^6]L(7)	$10752$	$1$		$-1$	$24$	$\GL(3,2)$	14T50, 28T388, 28T390 x 2, 42T613 x 2, 42T614 x 2, 42T615 x 2, 42T616 x 2

 

Results are complete for degrees $\leq 23$.