Properties

Label 15T36
Order \(1215\)
n \(15\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $15$
Transitive number $t$ :  $36$
CHM label :  $[3^{5}]5=3wr5$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15), (5,10,15)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
5:  $C_5$
15:  $C_{15}$
405:  15T26

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 5: $C_5$

Low degree siblings

15T36 x 15, 45T164 x 8, 45T165 x 16, 45T166 x 32, 45T167 x 32, 45T168 x 64, 45T169 x 64

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 63 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1215=3^{5} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1215, 69]
Character table: Data not available.