Galois group search results

Results (11 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
8T15	$Z_8 : Z_8^\times$	$32$	$-1$	✓	$3$	$11$	$C_2$, $D_{4}$	8T15, 16T35, 16T38 x 2, 16T45, 32T21
8T16	$(C_8:C_2):C_2$	$32$	$-1$	✓	$3$	$11$	$C_2$, $C_4$	8T16, 16T36, 16T41 x 2, 32T22
8T17	$C_4\wr C_2$	$32$	$-1$	✓	$3$	$14$	$C_2$, $D_{4}$	8T17, 16T28, 16T42, 32T14
8T18	$C_2^2 \wr C_2$	$32$	$1$	✓	$2$	$14$	$C_2$, $D_{4}$ x 3	8T18 x 7, 16T39 x 6, 16T46, 32T24
8T19	$C_2^3 : C_4 $	$32$	$1$	✓	$3$	$11$	$C_2$, $D_{4}$	8T19, 8T20, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T20	$C_2^3: C_4$	$32$	$1$	✓	$3$	$11$	$C_2$, $C_4$	8T19 x 2, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T21	$C_2^3: C_4$	$32$	$-1$	✓	$3$	$11$	$C_2$ x 3, $C_2^2$	8T19 x 2, 8T20, 16T33 x 2, 16T52, 16T53, 32T19
8T22	$Q_8:C_2^2$	$32$	$1$	✓	$2$	$17$	$C_2$ x 3, $C_2^2$	8T22 x 5, 16T23 x 9, 32T9
8T23	$\textrm{GL(2,3)}$	$48$	$-1$	✓	$-1$	$8$	$S_4$	8T23, 16T66, 24T22
8T24	$S_4\times C_2$	$48$	$1$	✓	$-1$	$10$	$C_2$, $S_4$	6T11 x 2, 8T24, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2
8T25	$C_2^3:C_7$	$56$	$1$	✓	$-1$	$8$		14T6, 28T11

 

Results are complete for degrees $\leq 23$.