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Properties

Label	29T7

Degree	$29$
Order	$4.421\times 10^{30}$
Cyclic	no
Abelian	no
Solvable	no
Primitive	yes
$p$ -group	no
Group:	$A_{29}$

Related objects

As an abstract group

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Show commands: Magma

magma: G := TransitiveGroup(29, 7);

Group invariants

Abstract group:		$A_{29}$	magma: IdentifyGroup(G);
Order:		$4420880996869850977271808000000=2^{24} \cdot 3^{13} \cdot 5^{6} \cdot 7^{4} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23 \cdot 29$	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);

Group action invariants

Degree $n$ :		$29$	magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$ :		$7$	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:		$(27,28,29)$ , $(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)$	magma: Generators(G);

Low degree resolvents

none
Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - 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

Conjugacy classes not computed

magma: ConjugacyClasses(G);

Character table

Character table not computed

magma: CharacterTable(G);

Regular extensions

Data not computed