Properties

Label 25T28
25T28 1 7 1->7 10 1->10 2 17 2->17 22 2->22 3 4 3->4 12 3->12 4->2 11 4->11 5 5->17 23 5->23 6 6->10 25 6->25 7->25 8 15 8->15 19 8->19 9 9->1 9->5 13 10->13 20 10->20 11->8 11->15 12->22 12->23 13->9 14 14->3 16 14->16 15->3 18 15->18 16->5 16->6 17->12 21 17->21 18->11 24 18->24 19->1 19->6 20->16 20->18 21->9 21->20 22->2 22->24 23->14 23->14 24->4 24->21 25->8 25->19
Degree 2525
Order 300300
Cyclic no
Abelian no
Solvable yes
Primitive yes
pp-group no
Group: C52:C3:C4C_5^2:C_3:C_4

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(25, 28);
 

Group invariants

Abstract group:  C52:C3:C4C_5^2:C_3:C_4
Copy content magma:IdentifyGroup(G);
 
Order:  300=22352300=2^{2} \cdot 3 \cdot 5^{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:  2525
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  2828
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  11
Copy content magma:IsEven(G);
 
Primitive:  yes
Copy content magma:IsPrimitive(G);
 
#Aut(F/K)\card{\Aut(F/K)}:  11
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,10,13,9)(2,17,12,22)(3,4,11,15)(5,23,14,16)(6,25,8,19)(18,24,21,20)(1,10,13,9)(2,17,12,22)(3,4,11,15)(5,23,14,16)(6,25,8,19)(18,24,21,20), (1,7,25,19)(2,22,24,4)(3,12,23,14)(5,17,21,9)(6,10,20,16)(8,15,18,11)(1,7,25,19)(2,22,24,4)(3,12,23,14)(5,17,21,9)(6,10,20,16)(8,15,18,11)
Copy content magma:Generators(G);
 

Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
22C2C_2
44C4C_4
66S3S_3
1212C3:C4C_3 : C_4

Resolvents shown for degrees 47\leq 47

Subfields

Degree 5: None

Low degree siblings

15T17 x 2, 30T71 x 2

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 1251^{25} 11 11 00 ()()
2A 212,12^{12},1 2525 22 1212 (1,21)(2,25)(3,24)(4,23)(5,22)(6,16)(7,20)(8,19)(9,18)(10,17)(12,15)(13,14)( 1,21)( 2,25)( 3,24)( 4,23)( 5,22)( 6,16)( 7,20)( 8,19)( 9,18)(10,17)(12,15)(13,14)
3A 38,13^{8},1 5050 33 1616 (1,11,13)(2,10,18)(3,4,23)(5,17,8)(6,12,7)(9,24,22)(14,25,16)(15,19,21)( 1,11,13)( 2,10,18)( 3, 4,23)( 5,17, 8)( 6,12, 7)( 9,24,22)(14,25,16)(15,19,21)
4A1 46,14^{6},1 7575 44 1818 (1,17,21,10)(2,20,25,7)(3,18,24,9)(4,16,23,6)(5,19,22,8)(12,14,15,13)( 1,17,21,10)( 2,20,25, 7)( 3,18,24, 9)( 4,16,23, 6)( 5,19,22, 8)(12,14,15,13)
4A-1 46,14^{6},1 7575 44 1818 (1,10,21,17)(2,7,25,20)(3,9,24,18)(4,6,23,16)(5,8,22,19)(12,13,15,14)( 1,10,21,17)( 2, 7,25,20)( 3, 9,24,18)( 4, 6,23,16)( 5, 8,22,19)(12,13,15,14)
5A 555^{5} 1212 55 2020 (1,7,13,19,25)(2,8,14,20,21)(3,9,15,16,22)(4,10,11,17,23)(5,6,12,18,24)( 1, 7,13,19,25)( 2, 8,14,20,21)( 3, 9,15,16,22)( 4,10,11,17,23)( 5, 6,12,18,24)
5B 555^{5} 1212 55 2020 (1,8,15,17,24)(2,9,11,18,25)(3,10,12,19,21)(4,6,13,20,22)(5,7,14,16,23)( 1, 8,15,17,24)( 2, 9,11,18,25)( 3,10,12,19,21)( 4, 6,13,20,22)( 5, 7,14,16,23)
6A 64,16^{4},1 5050 66 2020 (1,22,11,9,13,24)(2,17,10,8,18,5)(3,12,4,7,23,6)(14,19,25,21,16,15)( 1,22,11, 9,13,24)( 2,17,10, 8,18, 5)( 3,12, 4, 7,23, 6)(14,19,25,21,16,15)

Malle's constant a(G)a(G):     1/121/12

Copy content magma:ConjugacyClasses(G);
 

Character table

1A 2A 3A 4A1 4A-1 5A 5B 6A
Size 1 25 50 75 75 12 12 50
2 P 1A 1A 3A 2A 2A 5A 5B 3A
3 P 1A 2A 1A 4A-1 4A1 5A 5B 2A
5 P 1A 2A 3A 4A1 4A-1 1A 1A 6A
Type
300.23.1a R 1 1 1 1 1 1 1 1
300.23.1b R 1 1 1 1 1 1 1 1
300.23.1c1 C 1 1 1 i i 1 1 1
300.23.1c2 C 1 1 1 i i 1 1 1
300.23.2a R 2 2 1 0 0 2 2 1
300.23.2b S 2 2 1 0 0 2 2 1
300.23.12a R 12 0 0 0 0 3 2 0
300.23.12b R 12 0 0 0 0 2 3 0

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed