# Properties

 Label 23T6 Degree $23$ Order $1.293\times 10^{22}$ Cyclic no Abelian no Solvable no Primitive yes $p$-group no Group: $A_{23}$

# Related objects

## Group action invariants

 Degree $n$: $23$ Transitive number $t$: $6$ Group: $A_{23}$ Parity: $1$ Primitive: yes Nilpotency class: $-1$ (not nilpotent) $|\Aut(F/K)|$: $1$ Generators: (1,2,3), (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)

## 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

There are 641 conjugacy classes of elements. Data not shown.

## Group invariants

 Order: $12926008369442488320000=2^{18} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ Cyclic: no Abelian: no Solvable: no GAP id: not available
 Character table: not available.