Properties

Label 15T46
Order \(2430\)
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 $t$ :  $46$
CHM label :  $[3^{5}]D(5)=3wrD(5)$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,4)(2,8)(3,12)(6,9)(7,13)(11,14), (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)
2:  $C_2$
3:  $C_3$
6:  $C_6$
10:  $D_{5}$
30:  $D_5\times C_3$
810:  15T34

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 5: $D_{5}$

Low degree siblings

15T46 x 7, 30T388 x 4, 30T391 x 8, 45T250 x 4, 45T251 x 4, 45T261 x 8, 45T262 x 16, 45T263 x 16

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 72 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2430=2 \cdot 3^{5} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.