Group action invariants
| Degree $n$ : | $26$ | |
| Transitive number $t$ : | $47$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,6,17,12,7,22,20)(2,13,5,18,11,8,21,19)(3,24,16,25,4,23,15,26)(9,10), (1,3,26,7,16,13,22,5)(2,4,25,8,15,14,21,6)(9,17,20,24,10,18,19,23) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5616: $\PSL(3,3)$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 13: $\PSL(3,3)$
Low degree siblings
26T47, 26T48 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy Classes
| 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, 2 $ | $1$ | $2$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)(25,26)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $117$ | $2$ | $( 1,12)( 2,11)( 3,21)( 4,22)( 5, 6)( 7,25)( 8,26)(13,14)(15,16)(17,24)(18,23) (19,20)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $117$ | $2$ | $( 1,11)( 2,12)( 3,22)( 4,21)( 7,26)( 8,25)( 9,10)(17,23)(18,24)$ |
| $ 4, 4, 4, 4, 4, 4, 1, 1 $ | $702$ | $4$ | $( 1,25,12, 7)( 2,26,11, 8)( 3,17,21,24)( 4,18,22,23)( 5,19, 6,20)(13,16,14,15)$ |
| $ 4, 4, 4, 4, 4, 4, 2 $ | $702$ | $4$ | $( 1,26,12, 8)( 2,25,11, 7)( 3,18,21,23)( 4,17,22,24)( 5,20, 6,19)( 9,10) (13,15,14,16)$ |
| $ 8, 8, 8, 1, 1 $ | $702$ | $8$ | $( 1, 3,25,17,12,21, 7,24)( 2, 4,26,18,11,22, 8,23)( 5,14,19,15, 6,13,20,16)$ |
| $ 8, 8, 8, 2 $ | $702$ | $8$ | $( 1, 4,25,18,12,22, 7,23)( 2, 3,26,17,11,21, 8,24)( 5,13,19,16, 6,14,20,15) ( 9,10)$ |
| $ 8, 8, 8, 1, 1 $ | $702$ | $8$ | $( 1,24, 7,21,12,17,25, 3)( 2,23, 8,22,11,18,26, 4)( 5,16,20,13, 6,15,19,14)$ |
| $ 8, 8, 8, 2 $ | $702$ | $8$ | $( 1,23, 7,22,12,18,25, 4)( 2,24, 8,21,11,17,26, 3)( 5,15,20,14, 6,16,19,13) ( 9,10)$ |
| $ 26 $ | $432$ | $26$ | $( 1,10,13,12, 7, 3, 6,19,22,16,26,17,23, 2, 9,14,11, 8, 4, 5,20,21,15,25,18,24 )$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1, 9,13,11, 7, 4, 6,20,22,15,26,18,23)( 2,10,14,12, 8, 3, 5,19,21,16,25,17, 24)$ |
| $ 26 $ | $432$ | $26$ | $( 1,21,11,17, 6,10,15, 8,23,19,13,25, 4, 2,22,12,18, 5, 9,16, 7,24,20,14,26, 3 )$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1,22,11,18, 6, 9,15, 7,23,20,13,26, 4)( 2,21,12,17, 5,10,16, 8,24,19,14,25, 3)$ |
| $ 26 $ | $432$ | $26$ | $( 1,24,18,25,15,21,20, 5, 4, 8,11,14, 9, 2,23,17,26,16,22,19, 6, 3, 7,12,13,10 )$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1,23,18,26,15,22,20, 6, 4, 7,11,13, 9)( 2,24,17,25,16,21,19, 5, 3, 8,12,14, 10)$ |
| $ 26 $ | $432$ | $26$ | $( 1, 3,26,14,20,24, 7,16, 9, 5,18,12,22, 2, 4,25,13,19,23, 8,15,10, 6,17,11,21 )$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1, 4,26,13,20,23, 7,15, 9, 6,18,11,22)( 2, 3,25,14,19,24, 8,16,10, 5,17,12, 21)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1 $ | $624$ | $3$ | $( 1,21,24)( 2,22,23)( 3,20,26)( 4,19,25)( 5, 9,18)( 6,10,17)( 7,11,15) ( 8,12,16)$ |
| $ 6, 6, 6, 6, 2 $ | $624$ | $6$ | $( 1,22,24, 2,21,23)( 3,19,26, 4,20,25)( 5,10,18, 6, 9,17)( 7,12,15, 8,11,16) (13,14)$ |
| $ 6, 6, 6, 2, 2, 2, 2 $ | $104$ | $6$ | $( 1, 4, 7, 2, 3, 8)( 5,14,16, 6,13,15)( 9,10)(11,21,26,12,22,25)(17,18)(19,20) (23,24)$ |
| $ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $104$ | $3$ | $( 1, 3, 7)( 2, 4, 8)( 5,13,16)( 6,14,15)(11,22,26)(12,21,25)$ |
| $ 6, 6, 3, 3, 2, 2, 2, 1, 1 $ | $936$ | $6$ | $( 1,26, 3,11, 7,22)( 2,25, 4,12, 8,21)( 5,16,13)( 6,15,14)( 9,10)(17,23) (18,24)$ |
| $ 6, 6, 6, 2, 2, 2, 1, 1 $ | $936$ | $6$ | $( 1,25, 3,12, 7,21)( 2,26, 4,11, 8,22)( 5,15,13, 6,16,14)(17,24)(18,23)(19,20)$ |
Group invariants
| Order: | $11232=2^{5} \cdot 3^{3} \cdot 13$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |