# Properties

 Label 10T44 Degree $10$ Order $1814400$ Cyclic no Abelian no Solvable no Primitive yes $p$-group no Group: $A_{10}$

# Related objects

## Group action invariants

 Degree $n$: $10$ Transitive number $t$: $44$ Group: $A_{10}$ CHM label: $A10$ Parity: $1$ Primitive: yes Nilpotency class: $-1$ (not nilpotent) $\card{\Aut(F/K)}$: $1$ Generators: (1,2)(3,4,5,6,7,8,9,10), (1,2,3)

## Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Degree 2: None

Degree 5: None

## Low degree siblings

45T1982

Siblings are shown with degree $\leq 47$

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

## Conjugacy classes

 Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $3, 1, 1, 1, 1, 1, 1, 1$ $240$ $3$ $( 4, 8,10)$ $7, 1, 1, 1$ $86400$ $7$ $(1,6,7,9,3,2,5)$ $7, 3$ $86400$ $21$ $( 1, 2, 9, 6, 5, 3, 7)( 4, 8,10)$ $7, 3$ $86400$ $21$ $( 1, 2, 9, 6, 5, 3, 7)( 4,10, 8)$ $3, 3, 3, 1$ $22400$ $3$ $( 2, 8, 3)( 4, 7,10)( 5, 6, 9)$ $9, 1$ $201600$ $9$ $( 2, 5, 7, 8, 6,10, 3, 9, 4)$ $2, 2, 1, 1, 1, 1, 1, 1$ $630$ $2$ $( 2,10)( 3, 6)$ $4, 2, 1, 1, 1, 1$ $18900$ $4$ $( 2, 6,10, 3)( 4, 7)$ $3, 2, 2, 1, 1, 1$ $25200$ $6$ $( 1, 9, 5)( 2,10)( 3, 6)$ $4, 3, 2, 1$ $151200$ $12$ $( 1, 5, 9)( 2, 3,10, 6)( 4, 7)$ $2, 2, 2, 2, 1, 1$ $4725$ $2$ $( 1, 3)( 4, 9)( 5, 8)( 6,10)$ $3, 3, 1, 1, 1, 1$ $8400$ $3$ $( 1,10, 5)( 3, 6, 8)$ $6, 2, 1, 1$ $151200$ $6$ $( 1, 8,10, 3, 5, 6)( 4, 9)$ $4, 4, 1, 1$ $56700$ $4$ $( 1, 7, 5, 6)( 2,10, 3, 8)$ $8, 2$ $226800$ $8$ $( 1, 8, 7, 2, 5,10, 6, 3)( 4, 9)$ $4, 2, 2, 2$ $18900$ $4$ $( 1, 9, 3, 4)( 2, 7)( 5, 6)( 8,10)$ $3, 3, 2, 2$ $25200$ $6$ $( 1, 3)( 2, 8, 6)( 4, 9)( 5, 7,10)$ $6, 4$ $151200$ $12$ $( 1, 9, 3, 4)( 2, 5, 8, 7, 6,10)$ $5, 1, 1, 1, 1, 1$ $6048$ $5$ $(2,6,7,3,9)$ $5, 3, 1, 1$ $120960$ $15$ $( 2, 7, 9, 6, 3)( 4, 8,10)$ $5, 5$ $72576$ $5$ $( 1, 8, 4,10, 5)( 2, 9, 3, 7, 6)$ $9, 1$ $201600$ $9$ $( 2, 8,10, 5, 9, 7, 6, 4, 3)$ $5, 2, 2, 1$ $90720$ $10$ $( 1,10)( 2, 3, 6, 9, 7)( 5, 8)$

## Group invariants

 Order: $1814400=2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7$ Cyclic: no Abelian: no Solvable: no Label: not available
 Character table: not available.