Galois group search results

Results (1-50 of 96 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
26T1	$C_{26}$	$26$	$-1$	✓	$1$	$26$	$C_2$, $C_{13}$
26T2	$D_{13}$	$26$	$-1$	✓	$-1$	$8$	$C_2$, $D_{13}$	13T2
26T3	$D_{26}$	$52$	$-1$	✓	$-1$	$16$	$C_2$, $D_{13}$	26T3
26T4	$C_{13}:C_4$	$52$	$-1$	✓	$-1$	$7$	$C_2$, $C_{13}:C_4$	13T4
26T5	$C_{13}:C_6$	$78$	$-1$	✓	$-1$	$14$	$C_2$, $C_{13}:C_3$
26T6	$C_{13}:C_6$	$78$	$-1$	✓	$-1$	$8$	$C_2$, $C_{13}:C_6$	13T5, 39T6
26T7	$C_{26}:C_4$	$104$	$-1$	✓	$-1$	$14$	$C_2$, $C_{13}:C_4$	26T7
26T8	$F_{13}$	$156$	$-1$	✓	$-1$	$13$	$C_2$, $F_{13}$	13T6, 39T11
26T9	$C_{26}:C_6$	$156$	$-1$	✓	$-1$	$16$	$C_2$, $C_{13}:C_6$	26T9
26T10	$C_2\times F_{13}$	$312$	$-1$	✓	$-1$	$26$	$C_2$, $F_{13}$	26T10
26T11	$C_{13}\times D_{13}$	$338$	$-1$	✓	$-1$	$104$	$C_2$	26T11 x 5
26T12	$C_{13}^2:C_4$	$676$	$-1$	✓	$-1$	$46$	$C_2$	26T12 x 5
26T13	$D_{13}^2$	$676$	$-1$	✓	$-1$	$64$	$C_2$	26T13 x 5
26T14	$C_{13}^2:S_3$	$1014$	$-1$	✓	$-1$	$49$	$C_2$	39T26, 39T27
26T15	$C_{13}^2:C_6$	$1014$	$-1$	✓	$-1$	$40$	$C_2$	26T15 x 5
26T16	$D_{13}\wr C_2$	$1352$	$-1$	✓	$-1$	$44$	$C_2$	26T16, 26T19
26T17	$C_{13}^2:Q_8$	$1352$	$-1$	✓	$-1$	$26$	$C_2$	26T17 x 2
26T18	$D_{13}^2.C_2$	$1352$	$-1$	✓	$-1$	$38$	$C_2$	26T18 x 5
26T19	$D_{13}\wr C_2$	$1352$	$-1$	✓	$-1$	$44$	$C_2$	26T16 x 2
26T20	$C_{13}^2:C_8$	$1352$	$1$	✓	$-1$	$29$	$C_2$	26T20 x 6
26T21	$C_{13}:F_{13}$	$2028$	$-1$	✓	$-1$	$26$	$C_2$	26T21 x 5
26T22	$D_{13}^2:C_3$	$2028$	$-1$	✓	$-1$	$32$	$C_2$	26T22 x 5
26T23	$C_{13}^2:D_6$	$2028$	$-1$	✓	$-1$	$38$	$C_2$	39T34 x 2
26T24	$C_{13}^2:C_3:C_4$	$2028$	$-1$	✓	$-1$	$20$	$C_2$	39T35 x 2
26T25	$D_{13}^2.C_2^2$	$2704$	$-1$	✓	$-1$	$34$	$C_2$	26T25 x 2
26T26	$C_{13}^2:\OD_{16}$	$2704$	$1$	✓	$-1$	$25$	$C_2$
26T27	$C_{13}^2:(C_3\times S_3)$	$3042$	$-1$	✓	$-1$	$35$	$C_2$	39T39, 39T40
26T28	$D_{13}^2:S_3$	$4056$	$-1$	✓	$-1$	$28$	$C_2$
26T29	$C_{13}^2:C_{24}$	$4056$	$1$	✓	$-1$	$31$	$C_2$	26T29 x 6
26T30	$C_{13}^2:(C_4\times S_3)$	$4056$	$-1$	✓	$-1$	$28$	$C_2$	39T42 x 2
26T31	$C_{13}^2:C_3:C_8$	$4056$	$1$	✓	$-1$	$19$	$C_2$
26T32	$D_{13}^2:C_6$	$4056$	$-1$	✓	$-1$	$28$	$C_2$	26T32, 26T37
26T33	$D_{13}:F_{13}$	$4056$	$-1$	✓	$-1$	$34$	$C_2$	26T33 x 5
26T34	$C_{13}^2:(C_3\times Q_8)$	$4056$	$-1$	✓	$-1$	$22$	$C_2$	26T34 x 2
26T35	$C_{13}^2:C_3:Q_8$	$4056$	$-1$	✓	$-1$	$16$	$C_2$
26T36	$C_{13}^2:D_{12}$	$4056$	$-1$	✓	$-1$	$34$	$C_2$
26T37	$D_{13}^2:C_6$	$4056$	$-1$	✓	$-1$	$28$	$C_2$	26T32 x 2
26T38	$D_{13}^2.D_4$	$5408$	$-1$	✓	$-1$	$35$	$C_2$
26T39	$\PSL(3,3)$	$5616$	$1$		$-1$	$12$	$\PSL(3,3)$	13T7 x 2, 26T39, 39T43 x 2
26T40	$C_{13}^2:(C_6\times S_3)$	$6084$	$-1$	✓	$-1$	$34$	$C_2$	39T46 x 2
26T41	$C_{13}^2:C_3:C_{12}$	$6084$	$-1$	✓	$-1$	$28$	$C_2$	39T45 x 2
26T42	$\PSL(2,25)$	$7800$	$1$		$-1$	$15$
26T43	$D_{13}\wr C_2:C_6$	$8112$	$-1$	✓	$-1$	$38$	$C_2$	26T43 x 2
26T44	$C_{13}^2:C_3:\OD_{16}$	$8112$	$1$	✓	$-1$	$23$	$C_2$
26T45	$D_{13}^2.C_{12}$	$8112$	$1$	✓	$-1$	$35$	$C_2$
26T46	$D_{13}^2.D_6$	$8112$	$-1$	✓	$-1$	$32$	$C_2$
26T47	$\GL(3,3)$	$11232$	$-1$		$-1$	$24$	$\PSL(3,3)$	26T47, 26T48 x 2
26T48	$\GL(3,3)$	$11232$	$-1$		$-1$	$24$	$C_2$, $\PSL(3,3)$	26T47 x 2, 26T48
26T49	$\SL(3,3):C_2$	$11232$	$-1$		$-1$	$15$	$C_2$
26T50	$C_{13}^2:C_3^2:Q_8$	$12168$	$-1$	✓	$-1$	$32$	$C_2$

 

Results are complete for degrees $\leq 23$.