Galois group search results

Results (1-50 of 59 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
22T1	$C_{22}$	$22$	$-1$	✓	$1$	$22$	$C_2$, $C_{11}$
22T2	$D_{11}$	$22$	$-1$	✓	$-1$	$7$	$C_2$, $D_{11}$	11T2
22T3	$D_{22}$	$44$	$-1$	✓	$-1$	$14$	$C_2$, $D_{11}$	22T3, 44T4
22T4	$F_{11}$	$110$	$-1$	✓	$-1$	$11$	$C_2$, $F_{11}$	11T4
22T5	$C_2\times C_{11}:C_5$	$110$	$-1$	✓	$-1$	$14$	$C_2$, $C_{11}:C_5$
22T6	$C_2\times F_{11}$	$220$	$-1$	✓	$-1$	$22$	$C_2$, $F_{11}$	22T6, 44T14
22T7	$C_{11}\times D_{11}$	$242$	$-1$	✓	$-1$	$77$	$C_2$	22T7 x 4
22T8	$C_{11}:D_{11}.C_2$	$484$	$1$	✓	$-1$	$34$	$C_2$	22T8 x 5, 44T28 x 6
22T9	$D_{11}^2$	$484$	$-1$	✓	$-1$	$49$	$C_2$	22T9 x 4, 44T29 x 5
22T10	$C_{11}^2:D_4$	$968$	$-1$	✓	$-1$	$35$	$C_2$	22T10, 44T39 x 2, 44T40 x 2, 44T41 x 2, 44T44 x 2
22T11	$C_{11}^2:C_{10}$	$1210$	$-1$	✓	$-1$	$25$	$C_2$	22T11 x 4
22T12	$C_{11}^2:D_5$	$1210$	$-1$	✓	$-1$	$31$	$C_2$
22T13	$C_2\times \PSL(2,11)$	$1320$	$-1$		$-1$	$16$	$C_2$, $\PSL(2,11)$	22T13, 24T2948
22T14	$\PSL(2,11).C_2$	$1320$	$-1$		$-1$	$13$	$C_2$	12T218, 24T2949
22T15	t22n15	$2420$	$-1$	✓	$-1$	$29$	$C_2$	22T15 x 4, 44T59 x 5
22T16	t22n16	$2420$	$1$	✓	$-1$	$14$	$C_2$	44T60
22T17	t22n17	$2420$	$-1$	✓	$-1$	$29$	$C_2$	44T61
22T18	t22n18	$2420$	$1$	✓	$-1$	$26$	$C_2$	22T18 x 5, 44T62 x 6
22T19	t22n19	$4840$	$-1$	✓	$-1$	$25$	$C_2$	44T81, 44T82, 44T83
22T20	t22n20	$4840$	$-1$	✓	$-1$	$31$	$C_2$	22T20, 44T84 x 2, 44T85 x 2, 44T86 x 2, 44T89 x 2
22T21	t22n21	$6050$	$-1$	✓	$-1$	$35$	$C_2$
22T22	$M_{11}$	$7920$	$1$		$-1$	$10$	$M_{11}$	11T6, 12T272
22T23	t22n23	$11264$	$1$	✓	$-1$	$104$	$C_{11}$	22T23 x 92, 44T116 x 31, 44T117 x 465, 44T118 x 465, 44T119 x 465, 44T120 x 465, 44T121 x 930, 44T122 x 930, 44T123 x 930, 44T124 x 930, 44T125 x 930, 44T126 x 930, 44T127 x 930, 44T128 x 930, 44T129 x 930, 44T130 x 930, 44T131 x 930, 44T132 x 930, 44T133 x 930, 44T134 x 930, 44T135 x 930
22T24	t22n24	$12100$	$1$	✓	$-1$	$46$	$C_2$	44T138
22T25	t22n25	$12100$	$-1$	✓	$-1$	$49$	$C_2$	44T139
22T26	t22n26	$15840$	$-1$		$-1$	$20$	$M_{11}$	22T27, 24T12204, 44T140
22T27	t22n27	$15840$	$-1$		$-1$	$20$	$C_2$, $M_{11}$	22T26, 24T12204, 44T140
22T28	t22n28	$22528$	$-1$	✓	$-1$	$208$	$C_{11}$	22T28 x 92, 44T146 x 93, 44T149 x 93, 44T150 x 465, 44T151 x 465, 44T152 x 465, 44T153 x 465, 44T154 x 465, 44T155 x 465, 44T156 x 930, 44T157 x 930, 44T158 x 930, 44T159 x 930, 44T160 x 930, 44T161 x 930, 44T162 x 930, 44T163 x 930, 44T164 x 930, 44T165 x 930, 44T166 x 930, 44T167 x 930, 44T168 x 930, 44T169 x 930, 44T170 x 930, 44T171 x 930, 44T172 x 930, 44T173 x 930, 44T174 x 930, 44T175 x 930, 44T176 x 930, 44T177 x 930, 44T178 x 930, 44T179 x 930, 44T180 x 930, 44T181 x 930, 44T182 x 930, 44T183 x 930, 44T184 x 930, 44T185 x 930, 44T186 x 930, 44T187 x 930, 44T188 x 930, 44T189 x 930, 44T190 x 930, 44T191 x 930, 44T192 x 930, 44T193 x 930, 44T194 x 930, 44T195 x 930, 44T196 x 930, 44T197 x 930, 44T198 x 930, 44T199 x 930, 44T200 x 930, 44T201 x 930, 44T202 x 930, 44T203 x 930
22T29	t22n29	$22528$	$-1$	✓	$-1$	$100$	$D_{11}$	22T29 x 30, 22T30 x 31, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155
22T30	t22n30	$22528$	$1$	✓	$-1$	$100$	$D_{11}$	22T29 x 31, 22T30 x 30, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155
22T31	t22n31	$24200$	$-1$	✓	$-1$	$77$	$C_2$	44T218, 44T219, 44T220
22T32	t22n32	$45056$	$-1$	✓	$-1$	$200$	$D_{11}$	22T32 x 61, 44T236 x 31, 44T239 x 31, 44T240 x 62, 44T241 x 62, 44T266 x 310, 44T267 x 310, 44T268 x 310, 44T269 x 31, 44T270 x 155, 44T271 x 155, 44T272 x 155, 44T273 x 310, 44T274 x 310, 44T275 x 310
22T33	t22n33	$56320$	$1$	✓	$-1$	$40$	$C_{11}:C_5$	22T33 x 2, 44T288
22T34	t22n34	$112640$	$1$	✓	$-1$	$44$	$F_{11}$	22T35, 44T312, 44T313, 44T316
22T35	t22n35	$112640$	$-1$	✓	$-1$	$44$	$F_{11}$	22T34, 44T312, 44T313, 44T316
22T36	t22n36	$112640$	$-1$	✓	$-1$	$80$	$C_{11}:C_5$	22T36 x 2, 44T314 x 3, 44T315 x 3
22T37	t22n37	$225280$	$-1$	✓	$-1$	$88$	$F_{11}$	22T37, 44T333, 44T336, 44T339 x 2, 44T340 x 2, 44T341
22T38	$M_{22}$	$443520$	$1$		$-1$	$12$
22T39	t22n39	$675840$	$1$		$-1$	$56$	$\PSL(2,11)$	22T39
22T40	t22n40	$871200$	$-1$		$-1$	$44$	$C_2$	22T40, 24T21362
22T41	t22n41	$887040$	$-1$		$-1$	$21$		44T405
22T42	t22n42	$1351680$	$-1$		$-1$	$112$	$\PSL(2,11)$	22T42, 44T433 x 2
22T43	t22n43	$8110080$	$1$		$-1$	$52$	$M_{11}$	22T43, 44T554
22T44	t22n44	$16220160$	$-1$		$-1$	$104$	$M_{11}$	22T44, 44T613, 44T615 x 2, 44T617 x 2
22T45	t22n45	$39916800$	$-1$		$-1$	$56$	$C_2$, $S_{11}$	11T8
22T46	t22n46	$39916800$	$-1$		$-1$	$62$	$C_2$, $A_{11}$
22T47	t22n47	$79833600$	$-1$		$-1$	$112$	$C_2$, $S_{11}$	22T47, 44T1258
22T48	t22n48	$125452800$	$-1$		$-1$	$65$	$C_2$	24T24600, 44T1454
22T49	t22n49	$20437401600$	$1$		$-1$	$200$	$A_{11}$
22T50	t22n50	$40874803200$	$-1$		$-1$	$376$	$S_{11}$	22T51, 44T1749

 

Results are complete for degrees $\leq 23$.