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 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	$D_{17}.C_2$	$68$	$-1$	✓	$-1$	$8$	$C_2$, $C_{17}:C_{4}$	17T3
34T5	$C_2\times D_{17}.C_2$	$136$	$-1$	✓	$-1$	$16$	$C_2$, $C_{17}:C_{4}$	34T5
34T6	$C_{17}:C_8$	$136$	$-1$	✓	$-1$	$10$	$C_2$, $C_{17}:C_{8}$	17T4
34T7	$C_2\times C_{17}:C_8$	$272$	$-1$	✓	$-1$	$20$	$C_2$, $C_{17}:C_{8}$	34T7
34T8	$F_{17}$	$272$	$-1$	✓	$-1$	$17$	$C_2$, $F_{17}$	17T5
34T9	$C_{17}:(C_2\times C_{16})$	$544$	$-1$	✓	$-1$	$34$	$C_2$, $F_{17}$	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	t34n13	$2312$	$-1$	✓	$-1$	$65$	$C_2$	34T15 x 2
34T14	t34n14	$2312$	$-1$	✓	$-1$	$41$	$C_2$	34T14 x 2
34T15	t34n15	$2312$	$-1$	✓	$-1$	$65$	$C_2$	34T13, 34T15
34T16	t34n16	$2312$	$-1$	✓	$-1$	$56$	$C_2$	34T16 x 7
34T17	t34n17	$2312$	$-1$	✓	$-1$	$44$	$C_2$	34T17 x 7
34T18	t34n18	$4352$	$1$	✓	$-1$	$32$	$C_{17}$	34T18 x 14
34T19	t34n19	$4624$	$-1$	✓	$-1$	$49$	$C_2$
34T20	t34n20	$4624$	$-1$	✓	$-1$	$25$	$C_2$
34T21	t34n21	$4624$	$-1$	✓	$-1$	$40$	$C_2$	34T21 x 7
34T22	t34n22	$4624$	$-1$	✓	$-1$	$34$	$C_2$	34T22 x 7
34T23	t34n23	$4624$	$-1$	✓	$-1$	$37$	$C_2$
34T24	t34n24	$4624$	$-1$	✓	$-1$	$46$	$C_2$	34T24 x 2
34T25	t34n25	$4624$	$-1$	✓	$-1$	$34$	$C_2$	34T26 x 2
34T26	t34n26	$4624$	$-1$	✓	$-1$	$34$	$C_2$	34T25, 34T26
34T27	t34n27	$8160$	$-1$		$-1$	$34$	$C_2$, $\PSL(2,16)$
34T28	t34n28	$8160$	$-1$		$-1$	$16$	$C_2$, $\PSL(2,16):C_2$	17T7
34T29	t34n29	$8704$	$-1$	✓	$-1$	$64$	$C_{17}$	34T29 x 14
34T30	t34n30	$8704$	$1$	✓	$-1$	$40$	$D_{17}$	34T30 x 14, 34T31 x 15
34T31	t34n31	$8704$	$-1$	✓	$-1$	$40$	$D_{17}$	34T30 x 15, 34T31 x 14
34T32	t34n32	$9248$	$-1$	✓	$-1$	$44$	$C_2$
34T33	t34n33	$9248$	$-1$	✓	$-1$	$20$	$C_2$
34T34	t34n34	$9248$	$-1$	✓	$-1$	$32$	$C_2$	34T34, 34T36
34T35	t34n35	$9248$	$-1$	✓	$-1$	$38$	$C_2$	34T35 x 2
34T36	t34n36	$9248$	$-1$	✓	$-1$	$32$	$C_2$	34T34 x 2
34T37	t34n37	$9248$	$-1$	✓	$-1$	$32$	$C_2$
34T38	t34n38	$9248$	$-1$	✓	$-1$	$38$	$C_2$
34T39	t34n39	$9248$	$-1$	✓	$-1$	$26$	$C_2$
34T40	t34n40	$9248$	$-1$	✓	$-1$	$44$	$C_2$
34T41	t34n41	$9248$	$-1$	✓	$-1$	$44$	$C_2$	34T41 x 7
34T42	t34n42	$9248$	$1$	✓	$-1$	$41$	$C_2$	34T42 x 8
34T43	t34n43	$16320$	$-1$		$-1$	$32$	$C_2$, $\PSL(2,16):C_2$	34T43
34T44	t34n44	$16320$	$-1$		$-1$	$17$	$C_2$, $\PSL(2,16):C_4$	17T8
34T45	t34n45	$17408$	$-1$	✓	$-1$	$80$	$D_{17}$	34T45 x 29
34T46	t34n46	$17408$	$1$	✓	$-1$	$32$	$C_{17}:C_{4}$	34T46 x 2, 34T47 x 3
34T47	t34n47	$17408$	$-1$	✓	$-1$	$32$	$C_{17}:C_{4}$	34T46 x 3, 34T47 x 2
34T48	t34n48	$18496$	$-1$	✓	$-1$	$40$	$C_2$
34T49	t34n49	$18496$	$-1$	✓	$-1$	$28$	$C_2$
34T50	t34n50	$18496$	$-1$	✓	$-1$	$37$	$C_2$

Results are complete for degrees $\leq 23$.