Galois group: 10T44

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

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 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.