Properties

Label 46T27
Order \(20401920\)
n \(46\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $46$
Transitive number $t$ :  $27$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,34,26)(2,33,25)(3,15,11,24,7,36)(4,16,12,23,8,35)(5,27,14)(6,28,13)(9,44,42,20,39,37)(10,43,41,19,40,38)(17,31)(18,32)(21,45)(22,46), (1,12,46,13,17,2,11,45,14,18)(3,8,5,10,29,4,7,6,9,30)(15,19,44,21,27,16,20,43,22,28)(23,42,32,36,25,24,41,31,35,26)(33,34)(37,38)(39,40)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
10200960:  $M_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: $M_{23}$

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44) (45,46)$
$ 7, 7, 7, 7, 7, 7, 1, 1, 1, 1 $ $728640$ $7$ $( 1,46, 5,24,39,37,36)( 2,45, 6,23,40,38,35)( 3,29,31,27,42, 7, 9) ( 4,30,32,28,41, 8,10)(13,18,16,21,25,33,43)(14,17,15,22,26,34,44)$
$ 14, 14, 14, 2, 2 $ $728640$ $14$ $( 1,45, 5,23,39,38,36, 2,46, 6,24,40,37,35)( 3,30,31,28,42, 8, 9, 4,29,32,27, 41, 7,10)(11,12)(13,17,16,22,25,34,43,14,18,15,21,26,33,44)(19,20)$
$ 7, 7, 7, 7, 7, 7, 1, 1, 1, 1 $ $728640$ $7$ $( 1,36,37,39,24, 5,46)( 2,35,38,40,23, 6,45)( 3, 9, 7,42,27,31,29) ( 4,10, 8,41,28,32,30)(13,43,33,25,21,16,18)(14,44,34,26,22,15,17)$
$ 14, 14, 14, 2, 2 $ $728640$ $14$ $( 1,35,37,40,24, 6,46, 2,36,38,39,23, 5,45)( 3,10, 7,41,27,32,29, 4, 9, 8,42, 28,31,30)(11,12)(13,44,33,26,21,15,18,14,43,34,25,22,16,17)(19,20)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $3795$ $2$ $( 1,29)( 2,30)( 3,36)( 4,35)( 5,27)( 6,28)( 7,39)( 8,40)( 9,37)(10,38)(11,20) (12,19)(23,41)(24,42)(31,46)(32,45)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $3795$ $2$ $( 1,30)( 2,29)( 3,35)( 4,36)( 5,28)( 6,27)( 7,40)( 8,39)( 9,38)(10,37)(11,19) (12,20)(13,14)(15,16)(17,18)(21,22)(23,42)(24,41)(25,26)(31,45)(32,46)(33,34) (43,44)$
$ 14, 14, 14, 2, 2 $ $728640$ $14$ $( 1,41,36,28,37,32,39,30,24, 4, 5,10,46, 8)( 2,42,35,27,38,31,40,29,23, 3, 6, 9,45, 7)(11,19)(12,20)(13,22,43,15,33,17,25,14,21,44,16,34,18,26)$
$ 14, 14, 7, 7, 2, 2 $ $728640$ $14$ $( 1,42,36,27,37,31,39,29,24, 3, 5, 9,46, 7)( 2,41,35,28,38,32,40,30,23, 4, 6, 10,45, 8)(11,20)(12,19)(13,21,43,16,33,18,25)(14,22,44,15,34,17,26)$
$ 14, 14, 14, 2, 2 $ $728640$ $14$ $( 1,28,39, 4,46,41,37,30, 5, 8,36,32,24,10)( 2,27,40, 3,45,42,38,29, 6, 7,35, 31,23, 9)(11,19)(12,20)(13,15,25,44,18,22,33,14,16,26,43,17,21,34)$
$ 14, 14, 7, 7, 2, 2 $ $728640$ $14$ $( 1,27,39, 3,46,42,37,29, 5, 7,36,31,24, 9)( 2,28,40, 4,45,41,38,30, 6, 8,35, 32,23,10)(11,20)(12,19)(13,16,25,43,18,21,33)(14,15,26,44,17,22,34)$
$ 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1 $ $680064$ $5$ $( 1, 3,27,15,29)( 2, 4,28,16,30)( 5,37,17,42,46)( 6,38,18,41,45) ( 9,34,36,26,11)(10,33,35,25,12)(13,32,21,43,19)(14,31,22,44,20)$
$ 10, 10, 10, 10, 2, 2, 2 $ $680064$ $10$ $( 1, 4,27,16,29, 2, 3,28,15,30)( 5,38,17,41,46, 6,37,18,42,45)( 7, 8) ( 9,33,36,25,11,10,34,35,26,12)(13,31,21,44,19,14,32,22,43,20)(23,24)(39,40)$
$ 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2 $ $56672$ $6$ $( 1,19, 5, 2,20, 6)( 3,13,37, 4,14,38)( 7,23,39, 8,24,40)( 9,10)(11,12) (15,21,42,16,22,41)(17,28,31,18,27,32)(25,26)(29,43,46,30,44,45)(33,34)(35,36)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $56672$ $3$ $( 1,20, 5)( 2,19, 6)( 3,14,37)( 4,13,38)( 7,24,39)( 8,23,40)(15,22,42) (16,21,41)(17,27,31)(18,28,32)(29,44,46)(30,43,45)$
$ 15, 15, 5, 5, 3, 3 $ $680064$ $15$ $( 1,46,22,27,37,20,29,42,31, 3, 5,44,15,17,14)( 2,45,21,28,38,19,30,41,32, 4, 6,43,16,18,13)( 7,39,24)( 8,40,23)( 9,11,26,36,34)(10,12,25,35,33)$
$ 30, 10, 6 $ $680064$ $30$ $( 1,45,22,28,37,19,29,41,31, 4, 5,43,15,18,14, 2,46,21,27,38,20,30,42,32, 3, 6,44,16,17,13)( 7,40,24, 8,39,23)( 9,12,26,35,34,10,11,25,36,33)$
$ 15, 15, 5, 5, 3, 3 $ $680064$ $15$ $( 1,44,42,27,14, 5,29,22,17, 3,20,46,15,31,37)( 2,43,41,28,13, 6,30,21,18, 4, 19,45,16,32,38)( 7,24,39)( 8,23,40)( 9,11,26,36,34)(10,12,25,35,33)$
$ 30, 10, 6 $ $680064$ $30$ $( 1,43,42,28,14, 6,29,21,17, 4,20,45,15,32,37, 2,44,41,27,13, 5,30,22,18, 3, 19,46,16,31,38)( 7,23,39, 8,24,40)( 9,12,26,35,34,10,11,25,36,33)$
$ 11, 11, 11, 11, 1, 1 $ $927360$ $11$ $( 1,24, 3,22,44,14,31,11,29,36, 7)( 2,23, 4,21,43,13,32,12,30,35, 8) ( 5,37,20,34,26,42,15, 9,17,27,39)( 6,38,19,33,25,41,16,10,18,28,40)$
$ 22, 22, 2 $ $927360$ $22$ $( 1,23, 3,21,44,13,31,12,29,35, 7, 2,24, 4,22,43,14,32,11,30,36, 8) ( 5,38,20,33,26,41,15,10,17,28,39, 6,37,19,34,25,42,16, 9,18,27,40)(45,46)$
$ 22, 22, 2 $ $927360$ $22$ $( 1, 8,36,30,11,32,14,43,22, 4,24, 2, 7,35,29,12,31,13,44,21, 3,23) ( 5,40,27,18, 9,16,42,25,34,19,37, 6,39,28,17,10,15,41,26,33,20,38)(45,46)$
$ 11, 11, 11, 11, 1, 1 $ $927360$ $11$ $( 1, 7,36,29,11,31,14,44,22, 3,24)( 2, 8,35,30,12,32,13,43,21, 4,23) ( 5,39,27,17, 9,15,42,26,34,20,37)( 6,40,28,18,10,16,41,25,33,19,38)$
$ 23, 23 $ $443520$ $23$ $( 1,42, 7,22,34, 9,24,17,26, 3,44,14,37,29,27,39,46, 5,15,36,31,11,20) ( 2,41, 8,21,33,10,23,18,25, 4,43,13,38,30,28,40,45, 6,16,35,32,12,19)$
$ 46 $ $443520$ $46$ $( 1,41, 7,21,34,10,24,18,26, 4,44,13,37,30,27,40,46, 6,15,35,31,12,20, 2,42, 8,22,33, 9,23,17,25, 3,43,14,38,29,28,39,45, 5,16,36,32,11,19)$
$ 46 $ $443520$ $46$ $( 1,19,11,32,36,16, 5,45,39,28,29,38,14,43, 3,25,17,23, 9,33,22, 8,42, 2,20, 12,31,35,15, 6,46,40,27,30,37,13,44, 4,26,18,24,10,34,21, 7,41)$
$ 23, 23 $ $443520$ $23$ $( 1,20,11,31,36,15, 5,46,39,27,29,37,14,44, 3,26,17,24, 9,34,22, 7,42) ( 2,19,12,32,35,16, 6,45,40,28,30,38,13,43, 4,25,18,23,10,33,21, 8,41)$
$ 6, 6, 6, 6, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1 $ $850080$ $6$ $( 1,37,39)( 2,38,40)( 3,44,36,26,17,27)( 4,43,35,25,18,28)( 5,14)( 6,13) ( 7,46,24,34,29,15)( 8,45,23,33,30,16)( 9,31)(10,32)(11,22,20)(12,21,19)$
$ 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2 $ $850080$ $6$ $( 1,38,39, 2,37,40)( 3,43,36,25,17,28)( 4,44,35,26,18,27)( 5,13)( 6,14) ( 7,45,24,33,29,16)( 8,46,23,34,30,15)( 9,32)(10,31)(11,21,20,12,22,19)(41,42)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2 $ $318780$ $4$ $( 1, 2)( 3,32, 9,35)( 4,31,10,36)( 5,18)( 6,17)( 7,23,37,28)( 8,24,38,27) (11,33,29,21)(12,34,30,22)(13,14)(15,45,26,40)(16,46,25,39)(19,44)(20,43) (41,42)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $318780$ $4$ $( 3,31, 9,36)( 4,32,10,35)( 5,17)( 6,18)( 7,24,37,27)( 8,23,38,28) (11,34,29,22)(12,33,30,21)(15,46,26,39)(16,45,25,40)(19,43)(20,44)$
$ 8, 8, 8, 8, 4, 4, 2, 2, 2 $ $1275120$ $8$ $( 1,13)( 2,14)( 3,38,31,28, 9, 8,36,23)( 4,37,32,27,10, 7,35,24)( 5,19,17,43) ( 6,20,18,44)(11,16,34,45,29,25,22,40)(12,15,33,46,30,26,21,39)(41,42)$
$ 8, 8, 8, 8, 4, 4, 2, 2, 1, 1 $ $1275120$ $8$ $( 1,14)( 2,13)( 3,37,31,27, 9, 7,36,24)( 4,38,32,28,10, 8,35,23)( 5,20,17,44) ( 6,19,18,43)(11,15,34,46,29,26,22,39)(12,16,33,45,30,25,21,40)$

Group invariants

Order:  $20401920=2^{8} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.