Galois Group: 10T36

• Label: 10T36
• Order: \(1920\)
• n: \(10\)
• Cyclic: No
• Abelian: No
• Solvable: No
• Primitive: No
• $p$-group: No
• Group: $C_2 \wr A_5$

Group action invariants

Degree $n$ :		$10$
Transitive number $t$ :		$36$
Group :		$C_2 \wr A_5$
CHM label :		$[2^{5}]A(5)$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(5,10), (2,4,10)(5,7,9), (1,3,5,7,9)(2,4,6,8,10)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$
60:	$A_5$
120:	$A_5\times C_2$
960:	$C_2^4 : A_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 5: $A_5$

Low degree siblings

20T224, 20T225, 20T230, 30T344, 30T354, 32T97741, 40T1576, 40T1578, 40T1585, 40T1586, 40T1597, 40T1598, 40T1644

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 $	$1$	$1$	$()$
$ 2, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$2$	$( 5,10)$
$ 2, 2, 1, 1, 1, 1, 1, 1 $	$10$	$2$	$( 2, 7)( 5,10)$
$ 2, 2, 2, 1, 1, 1, 1 $	$10$	$2$	$( 2, 7)( 4, 9)( 5,10)$
$ 2, 2, 2, 2, 1, 1 $	$5$	$2$	$( 1, 6)( 2, 7)( 4, 9)( 5,10)$
$ 2, 2, 2, 2, 2 $	$1$	$2$	$( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)$
$ 2, 2, 2, 2, 1, 1 $	$60$	$2$	$( 1, 2)( 3, 4)( 6, 7)( 8, 9)$
$ 2, 2, 2, 2, 2 $	$60$	$2$	$( 1, 2)( 3, 4)( 5,10)( 6, 7)( 8, 9)$
$ 4, 2, 2, 1, 1 $	$120$	$4$	$( 1, 7, 6, 2)( 3, 4)( 8, 9)$
$ 4, 2, 2, 2 $	$120$	$4$	$( 1, 7, 6, 2)( 3, 4)( 5,10)( 8, 9)$
$ 4, 4, 1, 1 $	$60$	$4$	$( 1, 7, 6, 2)( 3, 9, 8, 4)$
$ 4, 4, 2 $	$60$	$4$	$( 1, 7, 6, 2)( 3, 9, 8, 4)( 5,10)$
$ 3, 3, 1, 1, 1, 1 $	$80$	$3$	$( 1, 2, 3)( 6, 7, 8)$
$ 3, 3, 2, 1, 1 $	$80$	$6$	$( 1, 2, 3)( 5,10)( 6, 7, 8)$
$ 6, 1, 1, 1, 1 $	$80$	$6$	$( 1, 7, 8, 6, 2, 3)$
$ 6, 2, 1, 1 $	$80$	$6$	$( 1, 7, 8, 6, 2, 3)( 5,10)$
$ 3, 3, 2, 1, 1 $	$80$	$6$	$( 1, 2, 3)( 4, 9)( 6, 7, 8)$
$ 3, 3, 2, 2 $	$80$	$6$	$( 1, 2, 3)( 4, 9)( 5,10)( 6, 7, 8)$
$ 6, 2, 1, 1 $	$80$	$6$	$( 1, 7, 8, 6, 2, 3)( 4, 9)$
$ 6, 2, 2 $	$80$	$6$	$( 1, 7, 8, 6, 2, 3)( 4, 9)( 5,10)$
$ 5, 5 $	$192$	$5$	$( 1, 2, 3, 4, 5)( 6, 7, 8, 9,10)$
$ 10 $	$192$	$10$	$( 1, 2, 3, 4,10, 6, 7, 8, 9, 5)$
$ 5, 5 $	$192$	$5$	$( 1, 2, 3, 5, 4)( 6, 7, 8,10, 9)$
$ 10 $	$192$	$10$	$( 1, 2, 3,10, 9, 6, 7, 8, 5, 4)$

Group invariants

Order:		$1920=2^{7} \cdot 3 \cdot 5$
Cyclic:		No
Abelian:		No
Solvable:		No
GAP id:		Data not available

Character table: Data not available.