Galois group search results

Results (11 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
8T6	$D_{8}$	$16$	$-1$	✓	$3$	$7$	$C_2$, $D_{4}$	8T6, 16T13
8T8	$QD_{16}$	$16$	$-1$	✓	$3$	$7$	$C_2$, $D_{4}$	16T12
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
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
8T26	$(C_4^2 : C_2):C_2$	$64$	$-1$	✓	$3$	$16$	$C_2$, $D_{4}$	8T26 x 3, 16T135 x 2, 16T141 x 2, 16T142 x 2, 16T152 x 2, 32T147 x 2, 32T148 x 2, 32T155, 32T156
8T29	$(((C_4 \times C_2): C_2):C_2):C_2$	$64$	$1$	✓	$3$	$16$	$C_2$, $D_{4}$	8T29 x 5, 8T31 x 2, 16T127, 16T128 x 3, 16T129 x 3, 16T147, 16T149 x 6, 16T150 x 3, 32T136 x 3, 32T137 x 2, 32T163 x 3
8T31	$(((C_4 \times C_2): C_2):C_2):C_2$	$64$	$-1$	✓	$3$	$16$	$C_2$ x 3, $C_2^2$	8T29 x 6, 8T31, 16T127, 16T128 x 3, 16T129 x 3, 16T147, 16T149 x 6, 16T150 x 3, 32T136 x 3, 32T137 x 2, 32T163 x 3

 

Results are complete for degrees $\leq 23$.