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Properties

Label 26T42
26T42 1 19 1->19 21 1->21 2 6 2->6 10 2->10 3 3->1 8 3->8 4 4->2 17 4->17 5 9 5->9 5->21 22 6->22 23 6->23 7 14 7->14 24 7->24 8->7 20 8->20 9->4 11 9->11 16 10->16 25 10->25 11->8 15 11->15 12 12->16 18 12->18 13 13->6 13->24 14->23 14->25 15->20 15->22 16->1 16->12 17->2 17->11 18->5 18->14 19->13 26 19->26 20->3 20->26 21->5 21->12 22->18 22->19 23->7 23->13 24->10 24->17 25->3 25->9 26->4 26->15
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

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

Group invariants

Abstract group:  $\PSL(2,25)$
Copy content magma:IdentifyGroup(G);
 
Order:  $7800=2^{3} \cdot 3 \cdot 5^{2} \cdot 13$
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 $n$:  $26$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $42$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  yes
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,19,26,4,17,2,6,22,18,5,21,12,16)(3,8,7,14,23,13,24,10,25,9,11,15,20)$, $(1,21,5,9,4,2,10,16,12,18,14,25,3)(6,23,7,24,17,11,8,20,26,15,22,19,13)$
Copy content 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 $2^{12},1^{2}$ $325$ $2$ $12$ $( 1,19)( 2, 6)( 3,14)( 4,10)( 7,25)( 8,15)( 9,17)(11,18)(12,23)(13,26)(16,22)(20,24)$
3A $3^{8},1^{2}$ $650$ $3$ $16$ $( 1,25,26)( 2, 9,20)( 3, 8,10)( 4,14,15)( 6,17,24)( 7,13,19)(11,12,22)(16,18,23)$
4A $4^{6},1^{2}$ $650$ $4$ $18$ $( 1,20,19,24)( 2, 7, 6,25)( 3,18,14,11)( 4,22,10,16)( 8,23,15,12)( 9,13,17,26)$
5A $5^{5},1$ $312$ $5$ $20$ $( 1,17, 5,23,22)( 2,14, 4,18,16)( 3,15,21,24,13)( 7, 8,26, 9,10)(11,20,19,12,25)$
5B $5^{5},1$ $312$ $5$ $20$ $( 1,22,25,20,16)( 3,13,14, 9, 7)( 4,21,12,24,11)( 5,18,10,17, 8)( 6,15,26,19,23)$
6A $6^{4},1^{2}$ $650$ $6$ $20$ $( 1,13,25,19,26, 7)( 2,24, 9, 6,20,17)( 3, 4, 8,14,10,15)(11,16,12,18,22,23)$
12A1 $12^{2},1^{2}$ $650$ $12$ $22$ $( 1, 6,13,20,25,17,19, 2,26,24, 7, 9)( 3,12, 4,18, 8,22,14,23,10,11,15,16)$
12A5 $12^{2},1^{2}$ $650$ $12$ $22$ $( 1,17, 7,20,26, 6,19, 9,25,24,13, 2)( 3,22,15,18,10,12,14,16, 8,11, 4,23)$
13A1 $13^{2}$ $600$ $13$ $24$ $( 1,12, 9,21, 8,25,17, 3, 4,19, 2,15, 5)( 6,24,13, 7,26,22,16,10,23,14,18,11,20)$
13A2 $13^{2}$ $600$ $13$ $24$ $( 1, 9, 8,17, 4, 2, 5,12,21,25, 3,19,15)( 6,13,26,16,23,18,20,24, 7,22,10,14,11)$
13A3 $13^{2}$ $600$ $13$ $24$ $( 1,21,17,19, 5, 9,25, 4,15,12, 8, 3, 2)( 6, 7,16,14,20,13,22,23,11,24,26,10,18)$
13A4 $13^{2}$ $600$ $13$ $24$ $( 1, 8, 4, 5,21, 3,15, 9,17, 2,12,25,19)( 6,26,23,20, 7,10,11,13,16,18,24,22,14)$
13A5 $13^{2}$ $600$ $13$ $24$ $( 1,25, 2, 9, 3, 5, 8,19,12,17,15,21, 4)( 6,22,18,13,10,20,26,14,24,16,11, 7,23)$
13A6 $13^{2}$ $600$ $13$ $24$ $( 1,17, 5,25,15, 8, 2,21,19, 9, 4,12, 3)( 6,16,20,22,11,26,18, 7,14,13,23,24,10)$

Malle's constant $a(G)$:     $1/12$

Copy content 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 13A2 13A4 13A6 13A5 13A3 13A1
3 P 1A 2A 1A 4A 5A 5B 2A 4A 4A 13A3 13A6 13A4 13A1 13A2 13A5
5 P 1A 2A 3A 4A 1A 1A 6A 12A5 12A1 13A5 13A3 13A2 13A6 13A1 13A4
13 P 1A 2A 3A 4A 5A 5B 6A 12A1 12A5 1A 1A 1A 1A 1A 1A
Type
7800.a.1a R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
7800.a.13a R 13 1 1 −1 −2 3 1 −1 −1 0 0 0 0 0 0
7800.a.13b R 13 1 1 −1 3 −2 1 −1 −1 0 0 0 0 0 0
7800.a.24a1 R 24 0 0 0 −1 −1 0 0 0 −ζ13−1−ζ13 −ζ13−2−ζ132 −ζ13−3−ζ133 −ζ13−4−ζ134 −ζ13−5−ζ135 −ζ13−6−ζ136
7800.a.24a2 R 24 0 0 0 −1 −1 0 0 0 −ζ13−2−ζ132 −ζ13−4−ζ134 −ζ13−6−ζ136 −ζ13−5−ζ135 −ζ13−3−ζ133 −ζ13−1−ζ13
7800.a.24a3 R 24 0 0 0 −1 −1 0 0 0 −ζ13−3−ζ133 −ζ13−6−ζ136 −ζ13−4−ζ134 −ζ13−1−ζ13 −ζ13−2−ζ132 −ζ13−5−ζ135
7800.a.24a4 R 24 0 0 0 −1 −1 0 0 0 −ζ13−4−ζ134 −ζ13−5−ζ135 −ζ13−1−ζ13 −ζ13−3−ζ133 −ζ13−6−ζ136 −ζ13−2−ζ132
7800.a.24a5 R 24 0 0 0 −1 −1 0 0 0 −ζ13−5−ζ135 −ζ13−3−ζ133 −ζ13−2−ζ132 −ζ13−6−ζ136 −ζ13−1−ζ13 −ζ13−4−ζ134
7800.a.24a6 R 24 0 0 0 −1 −1 0 0 0 −ζ13−6−ζ136 −ζ13−1−ζ13 −ζ13−5−ζ135 −ζ13−2−ζ132 −ζ13−4−ζ134 −ζ13−3−ζ133
7800.a.25a R 25 1 1 1 0 0 1 1 1 −1 −1 −1 −1 −1 −1
7800.a.26a R 26 2 −1 2 1 1 −1 −1 −1 0 0 0 0 0 0
7800.a.26b R 26 −2 2 0 1 1 −2 0 0 0 0 0 0 0 0
7800.a.26c R 26 2 −1 −2 1 1 −1 1 1 0 0 0 0 0 0
7800.a.26d1 R 26 −2 −1 0 1 1 1 −ζ12−1−ζ12 ζ12−1+ζ12 0 0 0 0 0 0
7800.a.26d2 R 26 −2 −1 0 1 1 1 ζ12−1+ζ12 −ζ12−1−ζ12 0 0 0 0 0 0

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed