Properties

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

Related objects

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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 TypeSizeOrderRepresentative
$ 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.