Properties

Label 15T92
Order \(648000\)
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 $t$ :  $92$
CHM label :  $[A(5)^{3}]3=A(5)wr3$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (3,6)(9,12), (1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15), (3,6,9,12,15)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 5: None

Low degree siblings

18T911, 30T1895, 36T33201, 45T1672

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 55 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $648000=2^{6} \cdot 3^{4} \cdot 5^{3}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.