Properties

Label 12T47
12T47 1 2 1->2 4 1->4 5 1->5 2->5 6 2->6 7 2->7 10 2->10 3 3->6 3->7 12 3->12 4->5 8 4->8 4->8 11 4->11 5->8 5->10 9 6->9 6->10 7->4 7->10 7->11 7->11 8->1 8->7 8->12 9->12 10->1 10->2 10->11 11->2 11->3 11->8 12->4
Degree 1212
Order 7272
Cyclic no
Abelian no
Solvable yes
Primitive no
pp-group no
Group: PSU(3,2)\PSU(3,2)

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(12, 47);
 

Group invariants

Abstract group:  PSU(3,2)\PSU(3,2)
Copy content magma:IdentifyGroup(G);
 
Order:  72=233272=2^{3} \cdot 3^{2}
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree nn:  1212
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  4747
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
CHM label:   [(1/3.33):2]E(4)4[(1/3.3^{3}):2]E(4)_{4}
Parity:  11
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
#Aut(F/K)\card{\Aut(F/K)}:  11
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,2,5,10)(3,12)(4,11,8,7)(6,9)(1,2,5,10)(3,12)(4,11,8,7)(6,9), (1,5)(2,10)(4,8)(7,11)(1,5)(2,10)(4,8)(7,11), (1,4,5,8)(2,7,10,11)(3,6)(9,12)(1,4,5,8)(2,7,10,11)(3,6)(9,12), (2,6,10)(3,7,11)(4,8,12)(2,6,10)(3,7,11)(4,8,12)
Copy content magma:Generators(G);
 

Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
22C2C_2 x 3
44C22C_2^2
88Q8Q_8

Resolvents shown for degrees 47\leq 47

Subfields

Degree 2: C2C_2 x 3

Degree 3: None

Degree 4: C22C_2^2

Degree 6: None

Low degree siblings

9T14, 18T35 x 3, 24T82, 36T55

Siblings are shown with degree 47\leq 47

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

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A 1121^{12} 11 11 00 ()()
2A 24,142^{4},1^{4} 99 22 44 (1,9)(6,10)(7,11)(8,12)( 1, 9)( 6,10)( 7,11)( 8,12)
3A 33,133^{3},1^{3} 88 33 66 (1,9,5)(2,6,10)(3,11,7)( 1, 9, 5)( 2, 6,10)( 3,11, 7)
4A 42,224^{2},2^{2} 1818 44 88 (1,7,9,11)(2,4)(3,5)(6,12,10,8)( 1, 7, 9,11)( 2, 4)( 3, 5)( 6,12,10, 8)
4B 42,224^{2},2^{2} 1818 44 88 (1,2,5,10)(3,12)(4,11,8,7)(6,9)( 1, 2, 5,10)( 3,12)( 4,11, 8, 7)( 6, 9)
4C 42,224^{2},2^{2} 1818 44 88 (1,4)(2,3,10,7)(5,8,9,12)(6,11)( 1, 4)( 2, 3,10, 7)( 5, 8, 9,12)( 6,11)

Malle's constant a(G)a(G):     1/41/4

Copy content magma:ConjugacyClasses(G);
 

Character table

1A 2A 3A 4A 4B 4C
Size 1 9 8 18 18 18
2 P 1A 1A 3A 2A 2A 2A
3 P 1A 2A 1A 4A 4B 4C
Type
72.41.1a R 1 1 1 1 1 1
72.41.1b R 1 1 1 1 1 1
72.41.1c R 1 1 1 1 1 1
72.41.1d R 1 1 1 1 1 1
72.41.2a S 2 2 2 0 0 0
72.41.8a R 8 0 1 0 0 0

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed

Additional information

This is an elusive group.