Galois group search results

Results (24 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
4T1	$C_4$	$4$	$-1$	✓	$1$	$4$	$C_2$
4T2	$C_2^2$	$4$	$1$	✓	$1$	$4$	$C_2$ x 3
4T3	$D_{4}$	$8$	$-1$	✓	$2$	$5$	$C_2$	4T3, 8T4
4T4	$A_4$	$12$	$1$	✓	$-1$	$4$		6T4, 12T4
4T5	$S_4$	$24$	$-1$	✓	$-1$	$5$		6T7, 6T8, 8T14, 12T8, 12T9, 24T10
5T1	$C_5$	$5$	$1$	✓	$1$	$5$
5T2	$D_{5}$	$10$	$1$	✓	$-1$	$4$		10T2
5T3	$F_5$	$20$	$-1$	✓	$-1$	$5$		10T4, 20T5
6T1	$C_6$	$6$	$-1$	✓	$1$	$6$	$C_2$, $C_3$
6T2	$S_3$	$6$	$-1$	✓	$-1$	$3$	$C_2$, $S_3$	3T2
6T3	$D_{6}$	$12$	$-1$	✓	$-1$	$6$	$C_2$, $S_3$	6T3, 12T3
6T4	$A_4$	$12$	$1$	✓	$-1$	$4$	$C_3$	4T4, 12T4
6T5	$S_3\times C_3$	$18$	$-1$	✓	$-1$	$9$	$C_2$	9T4, 18T3
6T6	$A_4\times C_2$	$24$	$-1$	✓	$-1$	$8$	$C_3$	8T13, 12T6, 12T7, 24T9
6T7	$S_4$	$24$	$1$	✓	$-1$	$5$	$S_3$	4T5, 6T8, 8T14, 12T8, 12T9, 24T10
6T8	$S_4$	$24$	$-1$	✓	$-1$	$5$	$S_3$	4T5, 6T7, 8T14, 12T8, 12T9, 24T10
6T9	$S_3^2$	$36$	$-1$	✓	$-1$	$9$	$C_2$	9T8, 12T16, 18T9, 18T11 x 2, 36T13
6T10	$C_3^2:C_4$	$36$	$1$	✓	$-1$	$6$	$C_2$	6T10, 9T9, 12T17 x 2, 18T10, 36T14
6T11	$S_4\times C_2$	$48$	$-1$	✓	$-1$	$10$	$S_3$	6T11, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2
6T13	$C_3^2:D_4$	$72$	$-1$	✓	$-1$	$9$	$C_2$	6T13, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2
7T1	$C_7$	$7$	$1$	✓	$1$	$7$
7T2	$D_{7}$	$14$	$-1$	✓	$-1$	$5$		14T2
7T3	$C_7:C_3$	$21$	$1$	✓	$-1$	$5$		21T2
7T4	$F_7$	$42$	$-1$	✓	$-1$	$7$		14T4, 21T4, 42T4

 

Results are complete for degrees $\leq 23$.