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Properties

Label 46T4
Degree $46$
Order $506$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{23}:C_{22}$

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Show commands: Magma

magma: G := TransitiveGroup(46, 4);
 

Group action invariants

Degree $n$:  $46$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $4$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{23}:C_{22}$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $2$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,20,9,35,42,8,32,33,38,46,15)(2,19,10,36,41,7,31,34,37,45,16)(3,23,18,5,27,25,22,13,43,11,40)(4,24,17,6,28,26,21,14,44,12,39), (1,36,4,25,8,5,15,11,32,23,17,2,35,3,26,7,6,16,12,31,24,18)(9,41,20,37,39,30,33,13,21,27,44,10,42,19,38,40,29,34,14,22,28,43)(45,46)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  22T1
$253$:  $C_{23}:C_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: $C_{23}:C_{11}$

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

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $506=2 \cdot 11 \cdot 23$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  506.2
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);