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Properties

Label 17T10
Degree 1717
Order 3.557×10143.557\times 10^{14}
Cyclic no
Abelian no
Solvable no
Primitive yes
pp-group no
Group: S17S_{17}

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Show commands: Magma

magma: G := TransitiveGroup(17, 10);
 

Group action invariants

Degree nn:  1717
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  1010
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  S17S_{17}
Parity:  −1-1
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
#Aut⁡(F/K)\card{\Aut(F/K)}:  11
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17), (1,2)
magma: Generators(G);
 

Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
22:  C2C_2

Resolvents shown for degrees ≤47\leq 47

Subfields

Prime degree - none

Low degree siblings

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

Conjugacy classes

Conjugacy classes not computed

magma: ConjugacyClasses(G);
 

Group invariants

Order:  355687428096000=215⋅36⋅53⋅72⋅11⋅13⋅17355687428096000=2^{15} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  355687428096000.a
magma: IdentifyGroup(G);
 
Character table:    not computed

magma: CharacterTable(G);