Show commands:
Magma
magma: G := TransitiveGroup(26, 39);
Group action invariants
| Degree $n$: | $26$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $\PSL(3,3)$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,2)(3,23)(4,24)(5,6)(7,21)(8,22)(9,11)(10,12)(13,19)(14,20)(17,18)(25,26), (1,4,5,8,9,11,13,16,18,20,21,24,25)(2,3,6,7,10,12,14,15,17,19,22,23,26) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 13: $\PSL(3,3)$
Low degree siblings
13T7 x 2, 26T39, 39T43 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy classes
| Label | Cycle Type | Size | Order | Representative |
| $ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $117$ | $2$ | $( 1, 2)( 3, 4)( 7, 8)( 9,21)(10,22)(11,23)(12,24)(13,15)(14,16)(17,25)(18,26) (19,20)$ | |
| $ 4, 4, 4, 4, 4, 4, 1, 1 $ | $702$ | $4$ | $( 1, 7, 2, 8)( 3,19, 4,20)( 9,15,21,13)(10,16,22,14)(11,17,23,25)(12,18,24,26)$ | |
| $ 8, 8, 8, 2 $ | $702$ | $8$ | $( 1,20, 7, 3, 2,19, 8, 4)( 5, 6)( 9,26,15,12,21,18,13,24)(10,25,16,11,22,17, 14,23)$ | |
| $ 8, 8, 8, 2 $ | $702$ | $8$ | $( 1, 4, 8,19, 2, 3, 7,20)( 5, 6)( 9,24,13,18,21,12,15,26)(10,23,14,17,22,11, 16,25)$ | |
| $ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $104$ | $3$ | $( 1,14,21)( 2,13,22)( 3,26,15)( 4,25,16)( 9,18,19)(10,17,20)$ | |
| $ 6, 6, 6, 2, 2, 2, 1, 1 $ | $936$ | $6$ | $( 1,18,14,19,21, 9)( 2,17,13,20,22,10)( 3,16,26, 4,15,25)( 5,12)( 6,11)(23,24)$ | |
| $ 13, 13 $ | $432$ | $13$ | $( 1,10,20,16,18, 6,21,25, 3,12,23,14, 8)( 2, 9,19,15,17, 5,22,26, 4,11,24,13, 7)$ | |
| $ 13, 13 $ | $432$ | $13$ | $( 1, 3,16,14,21,10,12,18, 8,25,20,23, 6)( 2, 4,15,13,22, 9,11,17, 7,26,19,24, 5)$ | |
| $ 13, 13 $ | $432$ | $13$ | $( 1, 8,14,23,12, 3,25,21, 6,18,16,20,10)( 2, 7,13,24,11, 4,26,22, 5,17,15,19, 9)$ | |
| $ 13, 13 $ | $432$ | $13$ | $( 1, 6,23,20,25, 8,18,12,10,21,14,16, 3)( 2, 5,24,19,26, 7,17,11, 9,22,13,15, 4)$ | |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1 $ | $624$ | $3$ | $( 1,16,18)( 2,15,17)( 3,23,20)( 4,24,19)( 5,11,22)( 6,12,21)( 7,26, 9) ( 8,25,10)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $5616=2^{4} \cdot 3^{3} \cdot 13$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 5616.a | magma: IdentifyGroup(G);
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| Character table: |
| Size | |
| 2 P | |
| 3 P | |
| 13 P | |
| Type |
magma: CharacterTable(G);