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Properties

Label 23T5
Degree $23$
Order $10200960$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $M_{23}$

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Show commands: Magma

magma: G := TransitiveGroup(23, 5);
 

Group action invariants

Degree $n$:  $23$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $5$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $M_{23}$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
Nilpotency class:  $-1$ (not nilpotent)
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,7,12,16,19,21,6)(2,8,13,17,20,5,11)(3,9,14,18,4,10,15), (2,14,18,20,8)(3,7,12,13,19)(4,21,17,15,10)(5,11,16,6,9), (3,19)(4,14)(5,20)(6,10)(8,15)(11,18)(17,21)(22,23), (1,22)(2,10)(3,14)(4,17)(8,15)(9,11)(13,20)(19,21)
magma: Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

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 $ $1$ $1$ $()$
$ 11, 11, 1 $ $927360$ $11$ $( 1, 8,11,14,22, 6,15,18,19,17, 2)( 3, 7,21,20,23,13,12,10, 9,16, 5)$
$ 11, 11, 1 $ $927360$ $11$ $( 1, 2,17,19,18,15, 6,22,14,11, 8)( 3, 5,16, 9,10,12,13,23,20,21, 7)$
$ 5, 5, 5, 5, 1, 1, 1 $ $680064$ $5$ $( 1,12, 8,14, 2)( 3, 7,17,11,19)( 5,20, 9,13,23)( 6,16,18,22,21)$
$ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1 $ $56672$ $3$ $( 1,17,21)( 2, 7,22)( 3,18,14)( 4,10,15)( 6,12,11)( 8,19,16)$
$ 15, 5, 3 $ $680064$ $15$ $( 1, 6,19,14,22,17,12,16, 3, 2,21,11, 8,18, 7)( 4,15,10)( 5,20, 9,13,23)$
$ 15, 5, 3 $ $680064$ $15$ $( 1,11,16,14, 7,21,12,19,18, 2,17, 6, 8, 3,22)( 4,10,15)( 5,20, 9,13,23)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1 $ $3795$ $2$ $( 1, 3)( 2,23)( 5,10)( 9,16)(11,12)(13,14)(19,22)(20,21)$
$ 4, 4, 4, 4, 2, 2, 1, 1, 1 $ $318780$ $4$ $( 1,16, 3, 9)( 2,19,23,22)( 5,11,10,12)( 6,15)( 8,17)(13,20,14,21)$
$ 8, 8, 4, 2, 1 $ $1275120$ $8$ $( 1,13,16,20, 3,14, 9,21)( 2,12,19, 5,23,11,22,10)( 6, 8,15,17)( 7,18)$
$ 7, 7, 7, 1, 1 $ $728640$ $7$ $( 1, 3, 8, 6,12, 7,11)( 2,13,20,14, 9,21,16)( 5,17,10,22,19,18,15)$
$ 7, 7, 7, 1, 1 $ $728640$ $7$ $( 1,11, 7,12, 6, 8, 3)( 2,16,21, 9,14,20,13)( 5,15,18,19,22,10,17)$
$ 14, 7, 2 $ $728640$ $14$ $( 1,12, 3, 7, 8,11, 6)( 2,10,13,22,20,19,14,18, 9,15,21, 5,16,17)( 4,23)$
$ 14, 7, 2 $ $728640$ $14$ $( 1, 7, 6, 3,11,12, 8)( 2,22,14,15,16,10,20,18,21,17,13,19, 9, 5)( 4,23)$
$ 6, 6, 3, 3, 2, 2, 1 $ $850080$ $6$ $( 1,15, 8,22,18, 6)( 2, 4,21)( 3,20,11,10,16,19)( 5,12)( 7,14, 9)(13,23)$
$ 23 $ $443520$ $23$ $( 1,17,13,15, 9,14, 4,11,10, 8,23,22,16,21, 7,12, 5, 3,19, 2,18, 6,20)$
$ 23 $ $443520$ $23$ $( 1,20, 6,18, 2,19, 3, 5,12, 7,21,16,22,23, 8,10,11, 4,14, 9,15,13,17)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $10200960=2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Label:  10200960.a
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);