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

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.