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Magma
magma: G := TransitiveGroup(26, 42);
Group action invariants
| Degree $n$: | $26$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $42$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $\PSL(2,25)$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| 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);
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Low degree resolvents
noneResolvents 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
| Label | Cycle Type | Size | Order | Representative |
| $1^{26}$ | $1$ | $1$ | $()$ | |
| $2^{12},1^{2}$ | $325$ | $2$ | $( 1,21)( 2, 9)( 3, 4)( 5,20)( 6,12)( 7,23)( 8,14)(11,18)(13,22)(16,17)(19,24) (25,26)$ | |
| $4^{6},1^{2}$ | $650$ | $4$ | $( 1, 9,21, 2)( 3, 8, 4,14)( 5,25,20,26)( 6,16,12,17)( 7,22,23,13)(11,19,18,24)$ | |
| $3^{8},1^{2}$ | $650$ | $3$ | $( 1, 5,24)( 2,26,18)( 3, 6, 7)( 4,12,23)( 8,16,22)( 9,25,11)(13,14,17) (19,21,20)$ | |
| $6^{4},1^{2}$ | $650$ | $6$ | $( 1,19, 5,21,24,20)( 2,11,26, 9,18,25)( 3,23, 6, 4, 7,12)( 8,13,16,14,22,17)$ | |
| $12^{2},1^{2}$ | $650$ | $12$ | $( 1,25,19, 2, 5,11,21,26,24, 9,20,18)( 3,16,23,14, 6,22, 4,17, 7, 8,12,13)$ | |
| $12^{2},1^{2}$ | $650$ | $12$ | $( 1,26,19, 9, 5,18,21,25,24, 2,20,11)( 3,17,23, 8, 6,13, 4,16, 7,14,12,22)$ | |
| $13^{2}$ | $600$ | $13$ | $( 1, 4,20,16,12, 9,17,14,10, 6,22,25,26)( 2, 8,23, 7, 5,11,15,21,19, 3,18,24, 13)$ | |
| $13^{2}$ | $600$ | $13$ | $( 1,10,16,25,17, 4, 6,12,26,14,20,22, 9)( 2,19, 7,24,15, 8, 3, 5,13,21,23,18, 11)$ | |
| $13^{2}$ | $600$ | $13$ | $( 1, 6, 9, 4,22,17,20,25,14,16,26,10,12)( 2, 3,11, 8,18,15,23,24,21, 7,13,19, 5)$ | |
| $13^{2}$ | $600$ | $13$ | $( 1,14, 4,10,20, 6,16,22,12,25, 9,26,17)( 2,21, 8,19,23, 3, 7,18, 5,24,11,13, 15)$ | |
| $13^{2}$ | $600$ | $13$ | $( 1,16,17, 6,26,20, 9,10,25, 4,12,14,22)( 2, 7,15, 3,13,23,11,19,24, 8, 5,21, 18)$ | |
| $13^{2}$ | $600$ | $13$ | $( 1,25, 6,14, 9,16, 4,26,22,10,17,12,20)( 2,24, 3,21,11, 7, 8,13,18,19,15, 5, 23)$ | |
| $5^{5},1$ | $312$ | $5$ | $( 1,14, 4,13,23)( 2, 5, 6, 7,25)( 3,19,12,26,10)( 8,16,24, 9,18) (11,17,20,22,15)$ | |
| $5^{5},1$ | $312$ | $5$ | $( 1,10, 9, 2,15)( 3,18, 5,11,14)( 4,19, 8, 6,17)( 7,20,13,12,16) (22,23,26,24,25)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $7800=2^{3} \cdot 3 \cdot 5^{2} \cdot 13$ | 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: | 7800.a | magma: IdentifyGroup(G);
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| Character table: |
| Size | |
| 2 P | |
| 3 P | |
| 5 P | |
| 13 P | |
| Type |
magma: CharacterTable(G);