Properties

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

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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 $\leq 47$

Subfields

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 TypeSizeOrderRepresentative
$ 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.