Galois group search results

Results (1-50 of 2113 matches)

 

Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
44T1	$C_{44}$	$44$	$-1$	✓	$1$	$44$	$C_2$, $C_4$, $C_{11}$, $C_{22}$
44T2	$C_2\times C_{22}$	$44$	$1$	✓	$1$	$44$	$C_2$ x 3, $C_2^2$, $C_{11}$, $C_{22}$ x 3
44T3	$C_{11}:C_4$	$44$	$-1$	✓	$-1$	$14$	$C_2$, $C_4$, $D_{11}$, $D_{11}$
44T4	$D_{22}$	$44$	$1$	✓	$-1$	$14$	$C_2$ x 3, $C_2^2$, $D_{11}$, $D_{11}$, $D_{22}$ x 2	22T3 x 2
44T5	$D_4\times C_{11}$	$88$	$-1$	✓	$2$	$55$	$C_2$, $D_{4}$, $C_{11}$, $C_{22}$	44T5
44T6	$C_{11}:D_4$	$88$	$-1$	✓	$-1$	$25$	$C_2$, $D_{4}$, $D_{11}$, $D_{11}$	44T8
44T7	$C_4\times D_{11}$	$88$	$-1$	✓	$-1$	$28$	$C_2$, $C_4$, $D_{11}$, $D_{22}$	44T7
44T8	$C_{11}:D_4$	$88$	$-1$	✓	$-1$	$25$	$C_2$, $D_{4}$, $D_{11}$, $D_{22}$	44T6
44T9	$D_{44}$	$88$	$-1$	✓	$-1$	$25$	$C_2$, $D_{4}$, $D_{11}$, $D_{22}$	44T9
44T10	$C_2\times D_{22}$	$88$	$1$	✓	$-1$	$28$	$C_2$ x 3, $C_2^2$, $D_{11}$, $D_{22}$ x 3	44T10 x 3
44T11	$C_{11}\times A_4$	$132$	$1$	✓	$-1$	$44$	$A_4$, $C_{11}$
44T12	$D_4\times D_{11}$	$176$	$-1$	✓	$-1$	$35$	$C_2$, $D_{4}$, $D_{11}$, $D_{22}$	44T12 x 3
44T13	$C_{11}:C_{20}$	$220$	$-1$	✓	$-1$	$22$	$C_2$, $C_4$, $F_{11}$, $F_{11}$
44T14	$C_2\times F_{11}$	$220$	$1$	✓	$-1$	$22$	$C_2$ x 3, $C_2^2$, $F_{11}$, $F_{11}$, $C_2\times F_{11}$ x 2	22T6 x 2
44T15	$C_{11}:C_{20}$	$220$	$-1$	✓	$-1$	$28$	$C_2$, $C_4$, $C_{11}:C_5$, $C_{11}:C_{10}$
44T16	$C_{22}:C_{10}$	$220$	$1$	✓	$-1$	$28$	$C_2$ x 3, $C_2^2$, $C_{11}:C_5$, $C_{11}:C_{10}$ x 3
44T17	$C_{11}\times S_4$	$264$	$-1$	✓	$-1$	$55$	$S_4$, $C_{11}$
44T18	$A_4\times D_{11}$	$264$	$1$	✓	$-1$	$28$	$A_4$, $D_{11}$
44T19	$C_{11}:S_4$	$264$	$-1$	✓	$-1$	$25$	$S_4$, $D_{11}$
44T20	$D_{22}:C_{10}$	$440$	$-1$	✓	$-1$	$29$	$C_2$, $D_{4}$, $F_{11}$, $F_{11}$	44T22
44T21	$C_{44}:C_{10}$	$440$	$-1$	✓	$-1$	$35$	$C_2$, $D_{4}$, $C_{11}:C_5$, $C_{11}:C_{10}$	44T21
44T22	$D_{22}:C_{10}$	$440$	$-1$	✓	$-1$	$29$	$C_2$, $D_{4}$, $F_{11}$, $C_2\times F_{11}$	44T20
44T23	$C_{44}:C_{10}$	$440$	$-1$	✓	$-1$	$29$	$C_2$, $D_{4}$, $F_{11}$, $C_2\times F_{11}$	44T23
44T24	$C_4\times F_{11}$	$440$	$-1$	✓	$-1$	$44$	$C_2$, $C_4$, $F_{11}$, $C_2\times F_{11}$	44T24
44T25	$C_2^2\times F_{11}$	$440$	$1$	✓	$-1$	$44$	$C_2$ x 3, $C_2^2$, $F_{11}$, $C_2\times F_{11}$ x 3	44T25 x 3
44T26	$C_{11}:C_{44}$	$484$	$-1$	✓	$-1$	$154$	$C_2$, $C_4$, $C_{11}\times D_{11}$	44T26 x 4
44T27	$C_{11}\times D_{22}$	$484$	$1$	✓	$-1$	$154$	$C_2$ x 3, $C_2^2$, $C_{11}\times D_{11}$	44T27 x 4
44T28	$C_{11}^2:C_4$	$484$	$-1$	✓	$-1$	$34$	$C_2$, $C_4$, $C_{11}^2:C_4$	22T8 x 6, 44T28 x 5
44T29	$D_{11}^2$	$484$	$1$	✓	$-1$	$49$	$C_2$ x 3, $C_2^2$, $D_{11}^2$	22T9 x 5, 44T29 x 4
44T30	$D_{11}\times S_4$	$528$	$-1$	✓	$-1$	$35$	$S_4$, $D_{11}$
44T31	$A_4\times C_{11}:C_5$	$660$	$1$	✓	$-1$	$28$	$A_4$, $C_{11}:C_5$
44T32	$D_4\times F_{11}$	$880$	$-1$	✓	$-1$	$55$	$C_2$, $D_{4}$, $F_{11}$, $C_2\times F_{11}$	44T32 x 3
44T33	$C_{22}\wr C_2$	$968$	$-1$	✓	$-1$	$275$	$C_2$, $D_{4}$, $C_{11}\times D_{11}$	44T33 x 9
44T34	$C_2\times C_{11}^2:C_4$	$968$	$-1$	✓	$-1$	$68$	$C_2$, $C_4$, $C_{11}^2:C_4$	44T34 x 5, 44T35 x 6
44T35	$C_2\times C_{11}^2:C_4$	$968$	$1$	✓	$-1$	$68$	$C_2$ x 3, $C_2^2$, $C_{11}^2:C_4$	44T34 x 6, 44T35 x 5
44T36	$C_{22}.D_{22}$	$968$	$-1$	✓	$-1$	$98$	$C_2$, $C_4$, $D_{11}^2$	44T36 x 9
44T37	$D_{11}\times D_{22}$	$968$	$1$	✓	$-1$	$98$	$C_2$ x 3, $C_2^2$, $D_{11}^2$	44T37 x 9
44T38	$C_{11}:D_{44}$	$968$	$-1$	✓	$-1$	$95$	$C_2$, $D_{4}$, $D_{11}^2$	44T38 x 9
44T39	$D_{11}\wr C_2$	$968$	$-1$	✓	$-1$	$35$	$C_2$, $D_{4}$, $D_{11}\wr C_2$	22T10 x 2, 44T39, 44T40 x 2, 44T41 x 2, 44T44 x 2
44T40	$D_{11}\wr C_2$	$968$	$1$	✓	$-1$	$35$	$C_2$ x 3, $C_2^2$, $D_{11}\wr C_2$	22T10 x 2, 44T39 x 2, 44T40, 44T41 x 2, 44T44 x 2
44T41	$D_{11}\wr C_2$	$968$	$-1$	✓	$-1$	$35$	$C_2$, $D_{4}$, $D_{11}\wr C_2$	22T10 x 2, 44T39 x 2, 44T40 x 2, 44T41, 44T44 x 2
44T42	$C_{11}^2:C_8$	$968$	$1$	✓	$-1$	$23$	$C_2$, $C_4$	44T42 x 2
44T43	$C_{11}^2:Q_8$	$968$	$1$	✓	$-1$	$20$	$C_2$ x 3, $C_2^2$	44T43 x 2
44T44	$D_{11}\wr C_2$	$968$	$1$	✓	$-1$	$35$	$C_2$ x 3, $C_2^2$	22T10 x 2, 44T39 x 2, 44T40 x 2, 44T41 x 2, 44T44
44T45	$C_{11}:C_5\times S_4$	$1320$	$-1$	✓	$-1$	$35$	$S_4$, $C_{11}:C_5$
44T46	$A_4\times F_{11}$	$1320$	$1$	✓	$-1$	$44$	$A_4$, $F_{11}$
44T47	$A_4:F_{11}$	$1320$	$-1$	✓	$-1$	$29$	$S_4$, $F_{11}$
44T48	$C_{22}^2:C_4$	$1936$	$-1$	✓	$-1$	$130$	$C_2$, $D_{4}$, $C_{11}^2:C_4$	44T48 x 23
44T49	$D_{22}:D_{22}$	$1936$	$-1$	✓	$-1$	$160$	$C_2$, $D_{4}$, $D_{11}^2$	44T49 x 19
44T50	$D_{11}^2:C_2^2$	$1936$	$1$	✓	$-1$	$70$	$C_2$ x 3, $C_2^2$, $D_{11}\wr C_2$	44T50 x 3, 44T53 x 4

 

Results are complete for degrees $\leq 23$.