LMFDB - Galois group: 31T12

Show commands: Magma

magma:G := TransitiveGroup(31, 12);

Group invariants

Abstract group:	$S_{31}$	magma:IdentifyGroup(G);
Order:	$8222838654177922817725562880000000=2^{26} \cdot 3^{14} \cdot 5^{7} \cdot 7^{4} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31$	magma:Order(G);
Cyclic:	no	magma:IsCyclic(G);
Abelian:	no	magma:IsAbelian(G);
Solvable:	no	magma:IsSolvable(G);
Nilpotency class:	not nilpotent	magma:NilpotencyClass(G);

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

$\card{(G/N)}$ Galois groups for stem field(s)
$2$ : $C_2$

Resolvents shown for degrees $\leq 47$

$\card{(G/N)}$	Galois groups for stem field(s)
$2$ :	$C_2$

Prime degree - none

There are no siblings with degree $\leq 47$

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

Conjugacy classes not computed

magma:ConjugacyClasses(G);

Character table not computed

magma:CharacterTable(G);

Data not computed

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