Galois group search results

Parity	Cyclic	Solvable	Primitive	Equivalent siblings
Degree	$T$-number	Order	Group	Nilpotency class

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Results (1-50 of 164 matches)

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
21T1	$C_{21}$	$21$	$1$	✓	$1$	$21$	$C_3$, $C_7$
21T2	$C_7:C_3$	$21$	$1$	✓	$-1$	$5$	$C_3$, $C_7:C_3$	7T3
21T3	$C_3\times D_7$	$42$	$-1$	✓	$-1$	$15$	$C_3$, $D_{7}$	42T3
21T4	$F_7$	$42$	$-1$	✓	$-1$	$7$	$C_3$, $F_7$	7T4, 14T4, 42T4
21T5	$D_{21}$	$42$	$1$	✓	$-1$	$12$	$S_3$, $D_{7}$	42T5
21T6	$C_7\times S_3$	$42$	$-1$	✓	$-1$	$21$	$S_3$, $C_7$	42T6
21T7	$C_3\times C_7:C_3$	$63$	$1$	✓	$-1$	$15$	$C_3$, $C_7:C_3$	21T7 x 2
21T8	$S_3\times D_7$	$84$	$-1$	✓	$-1$	$15$	$S_3$, $D_{7}$	42T13, 42T14, 42T15
21T9	$C_3\times F_7$	$126$	$-1$	✓	$-1$	$21$	$C_3$, $F_7$	21T9 x 2, 42T17 x 3
21T10	$D_{21}:C_3$	$126$	$1$	✓	$-1$	$12$	$S_3$, $F_7$	42T18, 42T22
21T11	$S_3\times C_7:C_3$	$126$	$-1$	✓	$-1$	$15$	$S_3$, $C_7:C_3$	42T19, 42T23
21T12	$C_7:(C_7:C_3)$	$147$	$1$	✓	$-1$	$19$	$C_3$	21T12
21T13	$C_7\times C_7:C_3$	$147$	$1$	✓	$-1$	$35$	$C_3$	21T13
21T14	$\PSL(2,7)$	$168$	$1$		$-1$	$6$	$\GL(3,2)$ x 2	7T5 x 2, 8T37, 14T10 x 2, 24T284, 28T32, 42T37, 42T38 x 2
21T15	$S_3\times F_7$	$252$	$-1$	✓	$-1$	$21$	$S_3$, $F_7$	42T43, 42T44, 42T45, 42T52
21T16	$C_7:(C_3\times D_7)$	$294$	$-1$	✓	$-1$	$22$	$C_3$	21T16, 42T55 x 2
21T17	$C_7^2:S_3$	$294$	$1$	✓	$-1$	$20$	$S_3$	14T15, 21T18, 42T56, 42T57, 42T62
21T18	$C_7^2:S_3$	$294$	$-1$	✓	$-1$	$20$	$S_3$	14T15, 21T17, 42T56, 42T57, 42T62
21T19	$C_7:D_7:C_3$	$294$	$-1$	✓	$-1$	$14$	$C_3$	21T19, 42T58 x 2
21T20	$\SO(3,7)$	$336$	$-1$		$-1$	$9$		8T43, 14T16, 16T713, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
21T21	$C_7^2:C_3:C_3$	$441$	$1$	✓	$-1$	$25$	$C_3$	21T21
21T22	$C_3\times \PSL(2,7)$	$504$	$1$		$-1$	$18$	$C_3$, $\GL(3,2)$	21T22, 24T1355 x 2, 24T1356, 42T96 x 2, 42T103 x 2
21T23	$C_7^2:D_6$	$588$	$-1$	✓	$-1$	$19$	$S_3$	14T25, 21T23, 28T78, 42T110 x 2, 42T111 x 2, 42T112 x 2, 42T122
21T24	$C_7^2:(C_3\times C_6)$	$882$	$-1$	✓	$-1$	$26$	$C_3$	21T24, 42T142 x 2
21T25	$C_7^2:(C_3\times S_3)$	$882$	$1$	✓	$-1$	$20$	$S_3$	14T26, 21T26, 42T143, 42T144, 42T152, 42T153, 42T154, 42T155
21T26	$C_7^2:(C_3\times S_3)$	$882$	$-1$	✓	$-1$	$20$	$S_3$	14T26, 21T25, 42T143, 42T144, 42T152, 42T153, 42T154, 42T155
21T27	$S_3\times \PSL(2,7)$	$1008$	$-1$		$-1$	$18$	$S_3$, $\GL(3,2)$	21T27, 24T2671, 42T169 x 2, 42T170 x 2, 42T171 x 2, 42T175 x 2
21T28	$C_7\times C_7:(C_7:C_3)$	$1029$	$1$	✓	$-1$	$133$	$C_3$	21T28 x 11
21T29	$C_7^2:(C_6\times S_3)$	$1764$	$-1$	✓	$-1$	$25$	$S_3$	14T37, 21T29, 28T170, 42T223 x 2, 42T224 x 2, 42T225 x 2, 42T252, 42T253, 42T254, 42T255
21T30	t21n30	$2058$	$1$	✓	$-1$	$77$	$S_3$	21T30 x 5, 42T267 x 6, 42T280 x 3, 42T283 x 2
21T31	t21n31	$2058$	$-1$	✓	$-1$	$71$	$C_3$	21T31 x 11, 42T268 x 12
21T32	t21n32	$2058$	$-1$	✓	$-1$	$140$	$S_3$	21T32 x 5, 42T269 x 6, 42T281 x 3, 42T282 x 2
21T33	$A_7$	$2520$	$1$		$-1$	$9$		7T6, 15T47 x 2, 35T28, 42T294, 42T299
21T34	t21n34	$3087$	$1$	✓	$-1$	$63$	$C_3$	21T34 x 11
21T35	t21n35	$3087$	$1$	✓	$-1$	$47$	$C_3$	21T35 x 18
21T36	t21n36	$4116$	$1$	✓	$-1$	$53$	$C_3$	28T275, 28T276 x 2, 42T390 x 2, 42T391, 42T406 x 2, 42T407
21T37	t21n37	$4116$	$-1$	✓	$-1$	$79$	$S_3$	21T37 x 5, 42T392 x 6, 42T393 x 6, 42T394 x 6, 42T400 x 3, 42T401 x 2
21T38	t21n38	$5040$	$-1$		$-1$	$15$		7T7, 14T46, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
21T39	t21n39	$5103$	$1$	✓	$-1$	$111$	$C_7$	21T39 x 51
21T40	t21n40	$6174$	$-1$	✓	$-1$	$60$	$S_3$	21T40 x 5, 42T464 x 6, 42T473 x 3, 42T474 x 2
21T41	t21n41	$6174$	$1$	✓	$-1$	$39$	$S_3$	21T41 x 5, 42T465 x 6, 42T472 x 3, 42T475 x 2
21T42	t21n42	$6174$	$-1$	✓	$-1$	$37$	$C_3$	21T42 x 18, 42T466 x 19
21T43	t21n43	$6174$	$-1$	✓	$-1$	$45$	$C_3$	21T43 x 11, 42T467 x 12
21T44	t21n44	$7560$	$1$		$-1$	$27$	$C_3$, $A_7$	45T442 x 2
21T45	t21n45	$8232$	$-1$	✓	$-1$	$55$	$C_3$	28T349, 28T350 x 2, 42T533, 42T534, 42T535 x 2, 42T536 x 2, 42T537, 42T545 x 2, 42T546
21T46	t21n46	$8232$	$-1$	✓	$-1$	$70$	$S_3$	28T347, 42T538, 42T539, 42T540, 42T548
21T47	t21n47	$8232$	$1$	✓	$-1$	$43$	$S_3$	28T348, 42T541, 42T542, 42T543, 42T547
21T48	t21n48	$9261$	$1$	✓	$-1$	$45$	$C_3$	21T48 x 3
21T49	t21n49	$9261$	$1$	✓	$-1$	$29$	$C_3$
21T50	t21n50	$10206$	$-1$	✓	$-1$	$66$	$C_7$	21T50 x 51, 42T554 x 52

Results are complete for degrees $\leq 23$.