Properties

Label 15T89
Order \(466560\)
n \(15\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $15$
Transitive number $t$ :  $89$
CHM label :  $1/2[S(3)^{5}]S(5)$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,4)(5,10)(6,9)(11,14), (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15), (5,10,15), (1,11)(4,14)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
120:  $S_5$
1920:  $(C_2^4:A_5) : C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 5: $S_5$

Low degree siblings

30T1810, 30T1824, 30T1833, 30T1834, 45T1514

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 60 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $466560=2^{7} \cdot 3^{6} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.