LMFDB - Galois group: 15T25

Show commands: Magma

magma:G := TransitiveGroup(15, 25);

Group invariants

Degree $n$ :	$15$	magma:t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$ :	$25$	magma:t, n := TransitiveGroupIdentification(G); t;
CHM label:	$[5^{3}]3=5wr3$
Parity:	$1$	magma:IsEven(G);
Primitive:	no	magma:IsPrimitive(G);
$\card{\Aut(F/K)}$ :	$5$	magma:Order(Centralizer(SymmetricGroup(n), G));
Generators:	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15)$ , $(3,6,9,12,15)$	magma:Generators(G);

$\card{(G/N)}$ Galois groups for stem field(s)
$3$ : $C_3$
$5$ : $C_5$
$15$ : $C_{15}$
$75$ : $C_5^2 : C_3$

Resolvents shown for degrees $\leq 47$

$\card{(G/N)}$	Galois groups for stem field(s)
$3$ :	$C_3$
$5$ :	$C_5$
$15$ :	$C_{15}$
$75$ :	$C_5^2 : C_3$

Degree 3: $C_3$
Degree 5: None

15T25 x 7
Siblings are shown with degree $\leq 47$

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

Conjugacy classes not computed

magma:ConjugacyClasses(G);

55 x 55 character table

magma:CharacterTable(G);

Data not computed

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