Group action invariants
| Degree $n$ : | $26$ | |
| Transitive number $t$ : | $48$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,23,19,22,8,14)(4,24,20,21,7,13)(5,6)(9,12,16,10,11,15)(17,25)(18,26), (1,15,24,12,25,6,19,17,13,10,3,7,21,2,16,23,11,26,5,20,18,14,9,4,8,22) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_2$
Degree 13: $\PSL(3,3)$
Low degree siblings
26T47 x 2, 26T48Siblings 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 $ | $1$ | $2$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)(25,26)$ |
| $ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $104$ | $3$ | $( 1, 5,25)( 2, 6,26)( 7,22,15)( 8,21,16)( 9,24,19)(10,23,20)$ |
| $ 6, 6, 6, 2, 2, 2, 2 $ | $104$ | $6$ | $( 1, 6,25, 2, 5,26)( 3, 4)( 7,21,15, 8,22,16)( 9,23,19,10,24,20)(11,12)(13,14) (17,18)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1 $ | $624$ | $3$ | $( 1,21, 9)( 2,22,10)( 3,11,13)( 4,12,14)( 5,16,24)( 6,15,23)( 7,20,26) ( 8,19,25)$ |
| $ 6, 6, 6, 6, 2 $ | $624$ | $6$ | $( 1,22, 9, 2,21,10)( 3,12,13, 4,11,14)( 5,15,24, 6,16,23)( 7,19,26, 8,20,25) (17,18)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $117$ | $2$ | $( 1,21)( 2,22)( 3,18)( 4,17)( 9,25)(10,26)(15,20)(16,19)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $117$ | $2$ | $( 1,22)( 2,21)( 3,17)( 4,18)( 5, 6)( 7, 8)( 9,26)(10,25)(11,12)(13,14)(15,19) (16,20)(23,24)$ |
| $ 6, 6, 3, 3, 2, 2, 1, 1, 1, 1 $ | $936$ | $6$ | $( 1, 3,25,21,18, 9)( 2, 4,26,22,17,10)( 7,23,12)( 8,24,11)(15,20)(16,19)$ |
| $ 6, 6, 6, 2, 2, 2, 2 $ | $936$ | $6$ | $( 1, 4,25,22,18,10)( 2, 3,26,21,17, 9)( 5, 6)( 7,24,12, 8,23,11)(13,14)(15,19) (16,20)$ |
| $ 4, 4, 4, 4, 2, 2, 2, 2, 1, 1 $ | $702$ | $4$ | $( 1,16,21,19)( 2,15,22,20)( 3, 9,18,25)( 4,10,17,26)( 5,24)( 6,23)( 7,12) ( 8,11)$ |
| $ 4, 4, 4, 4, 2, 2, 2, 2, 2 $ | $702$ | $4$ | $( 1,15,21,20)( 2,16,22,19)( 3,10,18,26)( 4, 9,17,25)( 5,23)( 6,24)( 7,11) ( 8,12)(13,14)$ |
| $ 8, 8, 4, 4, 1, 1 $ | $702$ | $8$ | $( 1,18,16,25,21, 3,19, 9)( 2,17,15,26,22, 4,20,10)( 5, 8,24,11)( 6, 7,23,12)$ |
| $ 8, 8, 4, 4, 2 $ | $702$ | $8$ | $( 1,17,16,26,21, 4,19,10)( 2,18,15,25,22, 3,20, 9)( 5, 7,24,12)( 6, 8,23,11) (13,14)$ |
| $ 8, 8, 4, 4, 1, 1 $ | $702$ | $8$ | $( 1, 9,19, 3,21,25,16,18)( 2,10,20, 4,22,26,15,17)( 5,11,24, 8)( 6,12,23, 7)$ |
| $ 8, 8, 4, 4, 2 $ | $702$ | $8$ | $( 1,10,19, 4,21,26,16,17)( 2, 9,20, 3,22,25,15,18)( 5,12,24, 7)( 6,11,23, 8) (13,14)$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1,18,21, 3,25, 8, 5,16, 9,24,13,11,19)( 2,17,22, 4,26, 7, 6,15,10,23,14,12, 20)$ |
| $ 26 $ | $432$ | $26$ | $( 1,17,21, 4,25, 7, 5,15, 9,23,13,12,19, 2,18,22, 3,26, 8, 6,16,10,24,14,11,20 )$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1, 9, 3,11, 5,18,24,25,19,16,21,13, 8)( 2,10, 4,12, 6,17,23,26,20,15,22,14, 7)$ |
| $ 26 $ | $432$ | $26$ | $( 1,10, 3,12, 5,17,24,26,19,15,21,14, 8, 2, 9, 4,11, 6,18,23,25,20,16,22,13, 7 )$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1,19,11,13,24, 9,16, 5, 8,25, 3,21,18)( 2,20,12,14,23,10,15, 6, 7,26, 4,22, 17)$ |
| $ 26 $ | $432$ | $26$ | $( 1,20,11,14,24,10,16, 6, 8,26, 3,22,18, 2,19,12,13,23, 9,15, 5, 7,25, 4,21,17 )$ |
| $ 13, 13 $ | $432$ | $13$ | $( 1, 8,13,21,16,19,25,24,18, 5,11, 3, 9)( 2, 7,14,22,15,20,26,23,17, 6,12, 4, 10)$ |
| $ 26 $ | $432$ | $26$ | $( 1, 7,13,22,16,20,25,23,18, 6,11, 4, 9, 2, 8,14,21,15,19,26,24,17, 5,12, 3,10 )$ |
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. |