Galois group search results

Results (1-50 of 115 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
34T1	$C_{34}$	$34$	$-1$	✓	$1$	$34$	$C_2$, $C_{17}$
34T2	$D_{17}$	$34$	$-1$	✓	$-1$	$10$	$C_2$, $D_{17}$	17T2
34T3	$D_{34}$	$68$	$-1$	✓	$-1$	$20$	$C_2$, $D_{17}$	34T3
34T4	$C_{17}:C_4$	$68$	$-1$	✓	$-1$	$8$	$C_2$, $C_{17}:C_{4}$	17T3
34T5	$C_{34}:C_4$	$136$	$-1$	✓	$-1$	$16$	$C_2$, $C_{17}:C_{4}$	34T5
34T6	$C_{17}:C_8$	$136$	$-1$	✓	$-1$	$10$	$C_2$, $C_{17}:C_{8}$	17T4
34T7	$C_{34}:C_8$	$272$	$-1$	✓	$-1$	$20$	$C_2$, $C_{17}:C_{8}$	34T7
34T8	$F_{17}$	$272$	$-1$	✓	$-1$	$17$	$C_2$, $F_{17}$	17T5
34T9	$C_2\times F_{17}$	$544$	$-1$	✓	$-1$	$34$	$C_2$, $F_{17}$	34T9
34T10	$C_{17}\times D_{17}$	$578$	$-1$	✓	$-1$	$170$	$C_2$	34T10 x 7
34T11	$D_{17}^2$	$1156$	$-1$	✓	$-1$	$100$	$C_2$	34T11 x 7
34T12	$C_{17}^2:C_4$	$1156$	$-1$	✓	$-1$	$76$	$C_2$	34T12 x 7
34T13	$D_{17}\wr C_2$	$2312$	$-1$	✓	$-1$	$65$	$C_2$	34T15 x 2
34T14	$C_{17}^2:Q_8$	$2312$	$-1$	✓	$-1$	$41$	$C_2$	34T14 x 2
34T15	$D_{17}\wr C_2$	$2312$	$-1$	✓	$-1$	$65$	$C_2$	34T13, 34T15
34T16	$D_{17}^2.C_2$	$2312$	$-1$	✓	$-1$	$56$	$C_2$	34T16 x 7
34T17	$C_{17}^2:C_8$	$2312$	$-1$	✓	$-1$	$44$	$C_2$	34T17 x 7
34T18	$C_2^8:C_{17}$	$4352$	$1$	✓	$-1$	$32$	$C_{17}$	34T18 x 14
34T19	$C_{17}^2:D_8$	$4624$	$-1$	✓	$-1$	$49$	$C_2$
34T20	$C_{17}^2:Q_{16}$	$4624$	$-1$	✓	$-1$	$25$	$C_2$
34T21	$D_{17}^2.C_4$	$4624$	$-1$	✓	$-1$	$40$	$C_2$	34T21 x 7
34T22	$C_{17}:F_{17}$	$4624$	$-1$	✓	$-1$	$34$	$C_2$	34T22 x 7
34T23	$C_{17}^2:\SD_{16}$	$4624$	$-1$	✓	$-1$	$37$	$C_2$
34T24	$D_{17}^2.C_2^2$	$4624$	$-1$	✓	$-1$	$46$	$C_2$	34T24 x 2
34T25	$C_{17}^2:\OD_{16}$	$4624$	$-1$	✓	$-1$	$34$	$C_2$	34T26 x 2
34T26	$C_{17}^2:\OD_{16}$	$4624$	$-1$	✓	$-1$	$34$	$C_2$	34T25, 34T26
34T27	$C_2\times \SL(2,16)$	$8160$	$-1$		$-1$	$34$	$C_2$, $\PSL(2,16)$
34T28	$\SOMinus(4,4)$	$8160$	$-1$		$-1$	$16$	$C_2$, $\PSL(2,16):C_2$	17T7
34T29	$C_2^9:C_{17}$	$8704$	$-1$	✓	$-1$	$64$	$C_{17}$	34T29 x 14
34T30	$C_2^8.D_{17}$	$8704$	$1$	✓	$-1$	$40$	$D_{17}$	34T30 x 14, 34T31 x 15
34T31	$C_2^8.D_{17}$	$8704$	$-1$	✓	$-1$	$40$	$D_{17}$	34T30 x 15, 34T31 x 14
34T32	$C_{17}^2:D_{16}$	$9248$	$-1$	✓	$-1$	$44$	$C_2$
34T33	$C_{17}^2:Q_{32}$	$9248$	$-1$	✓	$-1$	$20$	$C_2$
34T34	$C_{17}^2:\OD_{32}$	$9248$	$-1$	✓	$-1$	$32$	$C_2$	34T34, 34T36
34T35	$D_{17}^2.(C_2\times C_4)$	$9248$	$-1$	✓	$-1$	$38$	$C_2$	34T35 x 2
34T36	$C_{17}^2:\OD_{32}$	$9248$	$-1$	✓	$-1$	$32$	$C_2$	34T34 x 2
34T37	$C_{17}^2:\SD_{32}$	$9248$	$-1$	✓	$-1$	$32$	$C_2$
34T38	$D_{17}^2.D_4$	$9248$	$-1$	✓	$-1$	$38$	$C_2$
34T39	$D_{17}^2.Q_8$	$9248$	$-1$	✓	$-1$	$26$	$C_2$
34T40	$D_{17}^2.D_4$	$9248$	$-1$	✓	$-1$	$44$	$C_2$
34T41	$D_{17}:F_{17}$	$9248$	$-1$	✓	$-1$	$44$	$C_2$	34T41 x 7
34T42	$C_{17}^2:C_{32}$	$9248$	$1$	✓	$-1$	$41$	$C_2$	34T42 x 8
34T43	$C_2\times \SOMinus(4,4)$	$16320$	$-1$		$-1$	$32$	$C_2$, $\PSL(2,16):C_2$	34T43
34T44	$\PSL(2,16).C_4$	$16320$	$-1$		$-1$	$17$	$C_2$, $\PSL(2,16):C_4$	17T8
34T45	$C_2^8.D_{34}$	$17408$	$-1$	✓	$-1$	$80$	$D_{17}$	34T45 x 29
34T46	$C_2^8.C_{17}:C_4$	$17408$	$1$	✓	$-1$	$32$	$C_{17}:C_{4}$	34T46 x 2, 34T47 x 3
34T47	$C_2^8.C_{17}:C_4$	$17408$	$-1$	✓	$-1$	$32$	$C_{17}:C_{4}$	34T46 x 3, 34T47 x 2
34T48	$D_{17}^2.D_8$	$18496$	$-1$	✓	$-1$	$40$	$C_2$
34T49	$D_{17}^2.Q_{16}$	$18496$	$-1$	✓	$-1$	$28$	$C_2$
34T50	$D_{17}^2.\OD_{16}$	$18496$	$-1$	✓	$-1$	$37$	$C_2$

 

Results are complete for degrees $\leq 23$.