# Properties

 Label 23T7 Degree $23$ Order $2.585\times 10^{22}$ Cyclic no Abelian no Solvable no Primitive yes $p$-group no Group: $S_{23}$

# Related objects

Show commands: Magma

magma: G := TransitiveGroup(23, 7);

## Group action invariants

 Degree $n$: $23$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $7$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $S_{23}$ 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: (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23) magma: Generators(G);

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

## Subfields

Prime degree - none

## Low degree siblings

46T44

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

## Conjugacy classes

There are 1,255 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);

## Group invariants

 Order: $25852016738884976640000=2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ magma: Order(G); Cyclic: no magma: IsCyclic(G); Abelian: no magma: IsAbelian(G); Solvable: no magma: IsSolvable(G); Label: 25852016738884976640000.a magma: IdentifyGroup(G);
 Character table: not available.

magma: CharacterTable(G);