Galois group search results

Results (17 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
14T22	$C_7^2:C_3:C_4$	$588$	$1$	✓	$-1$	$10$	$C_2$	28T75, 42T119, 42T125
14T23	$C_7^2:C_{12}$	$588$	$1$	✓	$-1$	$16$	$C_2$	14T23 x 3, 28T76 x 4, 42T120 x 4
14T24	$D_7:F_7$	$588$	$-1$	✓	$-1$	$19$	$C_2$	14T24 x 2, 28T77 x 3, 42T121 x 3
14T25	$C_7^2:D_6$	$588$	$-1$	✓	$-1$	$19$	$C_2$	21T23 x 2, 28T78, 42T110 x 2, 42T111 x 2, 42T112 x 2, 42T122
14T26	$C_7^2:(C_3\times S_3)$	$882$	$-1$	✓	$-1$	$20$	$C_2$	21T25, 21T26, 42T143, 42T144, 42T152, 42T153, 42T154, 42T155
14T27	$C_2^6:D_7$	$896$	$-1$	✓	$-1$	$20$	$D_{7}$	14T27 x 6, 14T28 x 7, 16T1078, 28T98, 28T105 x 7, 28T106 x 21, 28T107 x 21, 28T108 x 7, 28T109 x 7
14T28	$C_2^6:D_7$	$896$	$1$	✓	$-1$	$20$	$D_{7}$	14T27 x 7, 14T28 x 6, 16T1078, 28T98, 28T105 x 7, 28T106 x 21, 28T107 x 21, 28T108 x 7, 28T109 x 7
14T29	$C_2 \wr C_7$	$896$	$-1$	✓	$-1$	$32$	$C_7$	14T29 x 6, 28T104 x 7, 28T110 x 21, 28T111 x 42, 28T112 x 42, 28T113 x 21, 28T114 x 42, 28T115 x 42, 28T116 x 14, 28T117 x 42, 28T118 x 7
15T27	$C_5^2:(C_4\times S_3)$	$600$	$-1$	✓	$-1$	$16$	$S_3$	15T27, 25T43, 30T150 x 2, 30T153 x 2, 30T155 x 2
15T28	$S_6$	$720$	$1$		$-1$	$11$		6T16 x 2, 10T32, 12T183 x 2, 15T28, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96
15T29	$S_5 \times S_3$	$720$	$-1$		$-1$	$21$	$S_3$, $S_5$	18T227, 30T165, 30T167, 30T170, 30T174, 30T178, 36T1249, 36T1250, 36T1251, 45T94
15T30	$C_5^3:C_6$	$750$	$1$	✓	$-1$	$32$	$C_3$	15T30 x 7, 30T188 x 8
15T31	$C_5^2:D_{15}$	$750$	$-1$	✓	$-1$	$35$	$S_3$	15T31 x 3, 30T186 x 4, 30T187 x 2
15T32	$C_5\wr S_3$	$750$	$-1$	✓	$-1$	$65$	$S_3$	15T32 x 3, 30T184 x 4, 30T185 x 2
15T33	$C_3^4:C_{10}$	$810$	$-1$	✓	$-1$	$18$	$C_5$	15T33 x 7, 30T190 x 8, 45T118 x 2, 45T119 x 16, 45T120 x 8
15T34	$C_3^4:D_5$	$810$	$1$	✓	$-1$	$24$	$D_{5}$	15T34 x 3, 15T35 x 4, 30T191 x 4, 30T192 x 4, 45T121 x 8, 45T122 x 8, 45T123, 45T124
15T35	$C_3^4:D_5$	$810$	$-1$	✓	$-1$	$24$	$D_{5}$	15T34 x 4, 15T35 x 3, 30T191 x 4, 30T192 x 4, 45T121 x 8, 45T122 x 8, 45T123, 45T124

 

Results are complete for degrees $\leq 23$.