Galois group search results

Results (1-50 of 104 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
15T1	$C_{15}$	$15$	$1$	✓	$1$	$15$	$C_3$, $C_5$
15T2	$D_{15}$	$30$	$-1$	✓	$-1$	$9$	$S_3$, $D_{5}$	30T3
15T3	$D_5\times C_3$	$30$	$1$	✓	$-1$	$12$	$C_3$, $D_{5}$	30T4
15T4	$S_3 \times C_5$	$30$	$-1$	✓	$-1$	$15$	$S_3$, $C_5$	30T2
15T5	$A_5$	$60$	$1$		$-1$	$5$	$A_5$	5T4, 6T12, 10T7, 12T33, 20T15, 30T9
15T6	$C_{15} : C_4$	$60$	$1$	✓	$-1$	$9$	$S_3$, $F_5$	30T6
15T7	$D_5\times S_3$	$60$	$-1$	✓	$-1$	$12$	$S_3$, $D_{5}$	30T8, 30T10, 30T13
15T8	$F_5\times C_3$	$60$	$-1$	✓	$-1$	$15$	$C_3$, $F_5$	30T7
15T9	$C_5^2 : C_3$	$75$	$1$	✓	$-1$	$11$	$C_3$	15T9, 25T6
15T10	$S_5$	$120$	$1$		$-1$	$7$	$S_5$	5T5, 6T14, 10T12, 10T13, 12T74, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
15T11	$F_5 \times S_3$	$120$	$-1$	✓	$-1$	$15$	$S_3$, $F_5$	30T23, 30T24, 30T32
15T12	$(C_5^2 : C_3):C_2$	$150$	$1$	✓	$-1$	$10$	$C_3$	15T12, 25T15, 30T35 x 2
15T13	$(C_5^2 : C_3):C_2$	$150$	$-1$	✓	$-1$	$13$	$S_3$	15T14, 25T16, 30T37, 30T38
15T14	$(C_5^2 : C_3):C_2$	$150$	$-1$	✓	$-1$	$13$	$S_3$	15T13, 25T16, 30T37, 30T38
15T15	$\GL(2,4)$	$180$	$1$		$-1$	$15$	$A_5$	15T15, 15T16, 18T90, 30T45, 36T176, 45T16
15T16	$\GL(2,4)$	$180$	$1$		$-1$	$15$	$C_3$, $A_5$	15T15 x 2, 18T90, 30T45, 36T176, 45T16
15T17	$(C_5^2 : C_3):C_4$	$300$	$1$	✓	$-1$	$8$	$S_3$	15T17, 25T28, 30T71 x 2
15T18	$((C_5^2 : C_3):C_2):C_2$	$300$	$-1$	✓	$-1$	$14$	$S_3$	15T18, 25T27, 30T66 x 2, 30T72 x 2, 30T80 x 2
15T19	$(C_5^2 : C_4):C_3$	$300$	$-1$	✓	$-1$	$14$	$C_3$	15T19, 25T26, 30T78 x 2
15T20	$A_6$	$360$	$1$		$-1$	$7$		6T15 x 2, 10T26, 15T20, 20T89, 30T88 x 2, 36T555, 40T304, 45T49
15T21	$\GL(2,4):C_2$	$360$	$1$		$-1$	$12$	$S_5$	15T21, 15T22, 18T146, 30T89, 30T93 x 2, 30T101, 36T554, 45T45
15T22	$\GL(2,4):C_2$	$360$	$1$		$-1$	$12$	$S_3$, $S_5$	15T21 x 2, 18T146, 30T89, 30T93 x 2, 30T101, 36T554, 45T45
15T23	$A_5 \times S_3$	$360$	$-1$		$-1$	$15$	$S_3$, $A_5$	18T145, 30T85, 30T94, 30T102, 36T551, 36T552, 36T553, 45T40
15T24	$S_5 \times C_3$	$360$	$-1$		$-1$	$21$	$C_3$, $S_5$	18T144, 30T90, 30T98, 30T103, 36T550, 45T44
15T25	$C_5\wr C_3$	$375$	$1$	✓	$-1$	$55$	$C_3$	15T25 x 7
15T26	$C_3^4:C_5$	$405$	$1$	✓	$-1$	$21$	$C_5$	15T26 x 7, 45T61 x 2, 45T62 x 16, 45T63 x 8
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
15T36	$C_3\wr C_5$	$1215$	$1$	✓	$-1$	$63$	$C_5$	15T36 x 15, 45T164 x 8, 45T165 x 16, 45T166 x 32, 45T167 x 32, 45T168 x 64, 45T169 x 64
15T37	$C_5\wr C_3:C_4$	$1500$	$1$	✓	$-1$	$19$	$S_3$	15T37 x 3, 30T282 x 2, 30T288 x 4
15T38	$C_5^3:C_{12}$	$1500$	$-1$	✓	$-1$	$25$	$C_3$	15T38 x 7, 30T287 x 8
15T39	$C_5^3:A_4$	$1500$	$1$	✓	$-1$	$28$	$C_3$	20T209, 30T271 x 2, 30T277, 30T279, 30T281
15T40	$C_5^3:D_6$	$1500$	$-1$	✓	$-1$	$40$	$S_3$	15T40 x 3, 30T273 x 4, 30T275 x 4, 30T280 x 2, 30T284 x 4
15T41	$C_3^4:F_5$	$1620$	$-1$	✓	$-1$	$21$	$F_5$	15T42, 30T295, 30T296, 30T298, 30T299, 30T302, 45T204, 45T210
15T42	$C_3^4:F_5$	$1620$	$1$	✓	$-1$	$21$	$F_5$	15T41, 30T295, 30T296, 30T298, 30T299, 30T302, 45T204, 45T210
15T43	$C_3^4:D_{10}$	$1620$	$-1$	✓	$-1$	$24$	$D_{5}$	15T43 x 7, 30T290 x 8, 30T291 x 8, 30T297 x 8, 45T205 x 16, 45T206 x 2
15T44	$C_7^3:C_6$	$2430$	$-1$	✓	$-1$	$39$	$C_5$	15T44 x 15, 30T394 x 16, 45T253 x 8, 45T254 x 16, 45T255 x 32, 45T256 x 32, 45T257 x 64, 45T258 x 64
15T45	$C_3^4:D_{15}$	$2430$	$-1$	✓	$-1$	$45$	$D_{5}$	15T45 x 7, 30T389 x 8, 30T392 x 4, 45T248 x 4, 45T249 x 4, 45T259 x 16, 45T260 x 16, 45T264 x 8
15T46	$C_3\wr D_5$	$2430$	$1$	✓	$-1$	$72$	$D_{5}$	15T46 x 7, 30T388 x 4, 30T391 x 8, 45T250 x 4, 45T251 x 4, 45T261 x 8, 45T262 x 16, 45T263 x 16
15T47	$A_7$	$2520$	$1$		$-1$	$9$		7T6, 15T47, 21T33, 35T28, 42T294, 42T299
15T48	$C_5^3:S_4$	$3000$	$-1$	✓	$-1$	$26$	$S_3$	20T270, 30T413, 30T424, 30T431, 30T432, 30T440, 40T2385
15T49	$C_9^2\times C_{54}$	$3000$	$-1$	✓	$-1$	$29$	$S_3$	15T49 x 3, 30T433 x 4, 30T435 x 2, 30T438 x 4, 30T442 x 4
15T50	$D_5\wr C_3$	$3000$	$1$	✓	$-1$	$32$	$C_3$	20T269, 30T408, 30T418, 30T419 x 2, 30T420 x 2, 30T421, 30T425, 30T426, 40T2384

 

Results are complete for degrees $\leq 23$.