Show commands:
Magma
magma: G := TransitiveGroup(26, 39);
Group action invariants
Degree $n$: | $26$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
Transitive number $t$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
Group: | $\PSL(3,3)$ | ||
Parity: | $1$ | magma: IsEven(G);
| |
Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
$\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
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);
|
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 | Index | Representative |
1A | $1^{26}$ | $1$ | $1$ | $0$ | $()$ |
2A | $2^{12},1^{2}$ | $117$ | $2$ | $12$ | $( 1,19)( 2,20)( 3, 4)( 5,24)( 6,23)( 9,26)(10,25)(11,12)(13,14)(15,22)(16,21)(17,18)$ |
3A | $3^{6},1^{8}$ | $104$ | $3$ | $12$ | $( 1,15,10)( 2,16, 9)( 3,17,14)( 4,18,13)(19,22,25)(20,21,26)$ |
3B | $3^{8},1^{2}$ | $624$ | $3$ | $16$ | $( 1,16,11)( 2,15,12)( 3,25,19)( 4,26,20)( 5,14,17)( 6,13,18)( 7,24,22)( 8,23,21)$ |
4A | $4^{6},1^{2}$ | $702$ | $4$ | $18$ | $( 1, 5,22,11)( 2, 6,21,12)( 3,20,16,18)( 4,19,15,17)( 7,14, 8,13)( 9,26,10,25)$ |
6A | $6^{3},2^{3},1^{2}$ | $936$ | $6$ | $18$ | $( 1,25,15,19,10,22)( 2,26,16,20, 9,21)( 3,13,17, 4,14,18)( 5,24)( 6,23)(11,12)$ |
8A1 | $8^{3},2$ | $702$ | $8$ | $22$ | $( 1, 4, 5,19,22,15,11,17)( 2, 3, 6,20,21,16,12,18)( 7,10,14,25, 8, 9,13,26)(23,24)$ |
8A-1 | $8^{3},2$ | $702$ | $8$ | $22$ | $( 1,15, 5,17,22, 4,11,19)( 2,16, 6,18,21, 3,12,20)( 7, 9,14,26, 8,10,13,25)(23,24)$ |
13A1 | $13^{2}$ | $432$ | $13$ | $24$ | $( 1,22, 6,16,23,10,14, 3,19,26,17, 7,11)( 2,21, 5,15,24, 9,13, 4,20,25,18, 8,12)$ |
13A-1 | $13^{2}$ | $432$ | $13$ | $24$ | $( 1, 3,22,19, 6,26,16,17,23, 7,10,11,14)( 2, 4,21,20, 5,25,15,18,24, 8, 9,12,13)$ |
13A2 | $13^{2}$ | $432$ | $13$ | $24$ | $( 1,10,17, 6, 3,11,23,26,22,14, 7,16,19)( 2, 9,18, 5, 4,12,24,25,21,13, 8,15,20)$ |
13A-2 | $13^{2}$ | $432$ | $13$ | $24$ | $( 1,17, 3,23,22, 7,19,10, 6,11,26,14,16)( 2,18, 4,24,21, 8,20, 9, 5,12,25,13,15)$ |
Malle's constant $a(G)$: $1/12$
magma: ConjugacyClasses(G);
Group invariants
Order: | $5616=2^{4} \cdot 3^{3} \cdot 13$ | magma: Order(G);
| |
Cyclic: | no | magma: IsCyclic(G);
| |
Abelian: | no | magma: IsAbelian(G);
| |
Solvable: | no | magma: IsSolvable(G);
| |
Nilpotency class: | not nilpotent | ||
Label: | 5616.a | magma: IdentifyGroup(G);
| |
Character table: |
1A | 2A | 3A | 3B | 4A | 6A | 8A1 | 8A-1 | 13A1 | 13A-1 | 13A2 | 13A-2 | ||
Size | 1 | 117 | 104 | 624 | 702 | 936 | 702 | 702 | 432 | 432 | 432 | 432 | |
2 P | 1A | 1A | 3A | 3B | 2A | 3A | 4A | 4A | 13A1 | 13A-2 | 13A2 | 13A-1 | |
3 P | 1A | 2A | 1A | 1A | 4A | 2A | 8A1 | 8A-1 | 13A-2 | 13A-1 | 13A1 | 13A2 | |
13 P | 1A | 2A | 3A | 3B | 4A | 6A | 8A-1 | 8A1 | 1A | 1A | 1A | 1A | |
Type |
magma: CharacterTable(G);