Properties

Label 46T27
Degree $46$
Order $20401920$
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)
$|\Aut(F/K)|$:  $2$
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)

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

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:  not available
Character table: not available.