# Properties

 Label 32T2801324 Degree $32$ Order $2.631\times 10^{35}$ Cyclic no Abelian no Solvable no Primitive yes $p$-group no Group: $S_{32}$

# Related objects

Show commands: Magma

magma: G := TransitiveGroup(32, 2801324);

## Group action invariants

 Degree $n$: $32$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $2801324$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $S_{32}$ Parity: $-1$ magma: IsEven(G); Primitive: yes magma: IsPrimitive(G); magma: NilpotencyClass(G); $\card{\Aut(F/K)}$: $1$ magma: Order(Centralizer(SymmetricGroup(n), G)); Generators: (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32), (1,2) magma: Generators(G);

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Degree 2: None

Degree 4: None

Degree 8: None

Degree 16: None

## Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

## Conjugacy classes

The 8349 conjugacy class representatives for $S_{32}$ are not computed

magma: ConjugacyClasses(G);

Malle's constant $a(G)$:     not computed

## Group invariants

 Order: $263130836933693530167218012160000000=2^{31} \cdot 3^{14} \cdot 5^{7} \cdot 7^{4} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31$ magma: Order(G); Cyclic: no magma: IsCyclic(G); Abelian: no magma: IsAbelian(G); Solvable: no magma: IsSolvable(G); Nilpotency class: not nilpotent Label: 263130836933693530167218012160000000.a magma: IdentifyGroup(G); Character table: not computed

magma: CharacterTable(G);