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Properties

Label 26T42
Degree $26$
Order $7800$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $\PSL(2,25)$

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Show commands: Magma

magma: G := TransitiveGroup(26, 42);
 

Group invariants

Abstract group:  $\PSL(2,25)$
magma: IdentifyGroup(G);
 
Order:  $7800=2^{3} \cdot 3 \cdot 5^{2} \cdot 13$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
magma: NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $26$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $42$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,19,26,4,17,2,6,22,18,5,21,12,16)(3,8,7,14,23,13,24,10,25,9,11,15,20)$, $(1,21,5,9,4,2,10,16,12,18,14,25,3)(6,23,7,24,17,11,8,20,26,15,22,19,13)$
magma: Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 13: None

Low degree siblings

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

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{26}$ $1$ $1$ $0$ $()$
2A $2^{12},1^{2}$ $325$ $2$ $12$ $( 1,11)( 3, 7)( 4,16)( 5,15)( 6,18)( 8,26)( 9,13)(10,23)(12,25)(17,19)(20,21)(22,24)$
3A $3^{8},1^{2}$ $650$ $3$ $16$ $( 2, 9,24)( 3, 5,14)( 4,25,16)( 6,20,17)( 7,10,22)( 8,12,26)(11,18,21)(13,23,15)$
4A $4^{6},1^{2}$ $650$ $4$ $18$ $( 1,19,11,17)( 3,13, 7, 9)( 4,18,16, 6)( 5,22,15,24)( 8,20,26,21)(10,25,23,12)$
5A $5^{5},1$ $312$ $5$ $20$ $( 2,15,10, 9,21)( 3,14,16,24,12)( 4,20, 8,11,18)( 5, 6,23,22,17)( 7,19,13,25,26)$
5B $5^{5},1$ $312$ $5$ $20$ $( 1,12, 8,13, 6)( 3,23,16,21,17)( 4,10, 7,19,20)( 5,14,15,22,24)( 9,26,25,11,18)$
6A $6^{4},1^{2}$ $650$ $6$ $20$ $( 2,20, 9,17,24, 6)( 3,11, 5,18,14,21)( 4, 8,25,12,16,26)( 7,15,10,13,22,23)$
12A1 $12^{2},1^{2}$ $650$ $12$ $22$ $( 2,18,20,14, 9,21,17, 3,24,11, 6, 5)( 4, 7, 8,15,25,10,12,13,16,22,26,23)$
12A5 $12^{2},1^{2}$ $650$ $12$ $22$ $( 2,21, 6,14,24,18,17, 5, 9,11,20, 3)( 4,10,26,15,16, 7,12,23,25,22, 8,13)$
13A1 $13^{2}$ $600$ $13$ $24$ $( 1, 3, 4,25,11,16,26, 9,14, 5,21,22,24)( 2,20, 7,17, 6,15,19, 8,18,10,23,13,12)$
13A2 $13^{2}$ $600$ $13$ $24$ $( 1,22, 5, 9,16,25, 3,24,21,14,26,11, 4)( 2,13,10, 8,15,17,20,12,23,18,19, 6, 7)$
13A3 $13^{2}$ $600$ $13$ $24$ $( 1,21, 9,11, 3,22,14,16, 4,24, 5,26,25)( 2,23, 8, 6,20,13,18,15, 7,12,10,19,17)$
13A4 $13^{2}$ $600$ $13$ $24$ $( 1,11,14,24,25, 9,22, 4,26,21, 3,16, 5)( 2, 6,18,12,17, 8,13, 7,19,23,20,15,10)$
13A5 $13^{2}$ $600$ $13$ $24$ $( 1,14,25,22,26, 3, 5,11,24, 9, 4,21,16)( 2,18,17,13,19,20,10, 6,12, 8, 7,23,15)$
13A6 $13^{2}$ $600$ $13$ $24$ $( 1, 9, 3,14, 4, 5,25,21,11,22,16,24,26)( 2, 8,20,18, 7,10,17,23, 6,13,15,12,19)$

Malle's constant $a(G)$:     $1/12$

magma: ConjugacyClasses(G);
 

Character table

1A 2A 3A 4A 5A 5B 6A 12A1 12A5 13A1 13A2 13A3 13A4 13A5 13A6
Size 1 325 650 650 312 312 650 650 650 600 600 600 600 600 600
2 P 1A 1A 3A 2A 5A 5B 3A 6A 6A 13A6 13A1 13A5 13A2 13A4 13A3
3 P 1A 2A 1A 4A 5A 5B 2A 4A 4A 13A4 13A5 13A1 13A3 13A6 13A2
5 P 1A 2A 3A 4A 1A 1A 6A 12A5 12A1 13A2 13A4 13A6 13A5 13A3 13A1
13 P 1A 2A 3A 4A 5A 5B 6A 12A1 12A5 1A 1A 1A 1A 1A 1A
Type

magma: CharacterTable(G);
 

Regular extensions

Data not computed