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Properties

Label 46T47
Degree 4646
Order 1.084×10291.084\times 10^{29}
Cyclic no
Abelian no
Solvable no
Primitive no
pp-group no
Group: C223.A23C_2^{23}.A_{23}

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Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 47);
 

Group invariants

Abstract group:  C223.A23C_2^{23}.A_{23}
Copy content magma:IdentifyGroup(G);
 
Order:  108431217215972213061058560000=241⋅39⋅54⋅73⋅112⋅13⋅17⋅19⋅23108431217215972213061058560000=2^{41} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree nn:  4646
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  4747
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  −1-1
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
#Aut⁡(F/K)\card{\Aut(F/K)}:  22
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,7,14,23,5,18,19,31,26,15,12,34,2,8,13,24,6,17,20,32,25,16,11,33)(3,38,44,9)(4,37,43,10)(21,40,46,30,22,39,45,29)(27,35,28,36)(1,7,14,23,5,18,19,31,26,15,12,34,2,8,13,24,6,17,20,32,25,16,11,33)(3,38,44,9)(4,37,43,10)(21,40,46,30,22,39,45,29)(27,35,28,36), (1,45,11,41,37,22,26,39,16,36,28,34,32,30,20,6,17)(2,46,12,42,38,21,25,40,15,35,27,33,31,29,19,5,18)(3,44,14,9,23)(4,43,13,10,24)(1,45,11,41,37,22,26,39,16,36,28,34,32,30,20,6,17)(2,46,12,42,38,21,25,40,15,35,27,33,31,29,19,5,18)(3,44,14,9,23)(4,43,13,10,24)
Copy content magma:Generators(G);
 

Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
22:  C2C_2
1292600836944248832000012926008369442488320000:  A23A_{23}
2585201673888497664000025852016738884976640000:  46T43
5421560860798610653052928000054215608607986106530529280000:  46T46

Resolvents shown for degrees ≤47\leq 47

Subfields

Degree 2: None

Degree 23: A23A_{23}

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

Copy content magma:ConjugacyClasses(G);
 

Character table

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed