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

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.