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Properties

Label 18T653
Degree 1818
Order 2624426244
Cyclic no
Abelian no
Solvable yes
Primitive no
pp-group no
Group: C3≀S32C_3\wr S_3^2

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Show commands: Magma

magma: G := TransitiveGroup(18, 653);
 

Group action invariants

Degree nn:  1818
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  653653
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  C3≀S32C_3\wr S_3^2
Parity:  −1-1
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
#Aut⁡(F/K)\card{\Aut(F/K)}:  33
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,11,15,16,7,5,2,10,14,18,9,4,3,12,13,17,8,6), (4,17)(5,18)(6,16)(7,14,8,15,9,13), (1,9)(2,8)(3,7)(4,5,6)(10,16,12,18,11,17)
magma: Generators(G);
 

Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
22:  C2C_2 x 3
33:  C3C_3
44:  C22C_2^2
66:  S3S_3 x 3, C6C_6 x 3
1212:  D6D_{6} x 3, C6×C2C_6\times C_2
1818:  S3×C3S_3\times C_3 x 3
3636:  S32S_3^2 x 3, C6×S3C_6\times S_3 x 3
108108:  12T70 x 3, 12T71
324324:  12T130
972972:  27T271 x 2
29162916:  18T409
87488748:  27T726, 27T791

Resolvents shown for degrees ≤47\leq 47

Subfields

Degree 2: C2C_2

Degree 3: None

Degree 6: S32S_3^2

Degree 9: None

Low degree siblings

18T653 x 8, 36T12787 x 9, 36T12879 x 9

Siblings are shown 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:  26244=22⋅3826244=2^{2} \cdot 3^{8}
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  26244.dw
magma: IdentifyGroup(G);
 
Character table:    not computed

magma: CharacterTable(G);