Properties

Label 15T78
Degree $15$
Order $29160$
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 $t$:  $78$
CHM label:  $[3^{5}]S(5)=3wrS(5)$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $3$
Generators:  (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15), (5,10,15), (1,4)(6,9)(11,14)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$120$:  $S_5$
$360$:  $S_5 \times C_3$
$9720$:  15T63

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 5: $S_5$

Low degree siblings

15T78, 30T1016 x 2, 30T1033 x 2, 30T1038 x 2, 45T696 x 2, 45T723

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 108 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $29160=2^{3} \cdot 3^{6} \cdot 5$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.