Group action invariants
| Degree $n$: | $26$ | |
| Transitive number $t$: | $15$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,23,3,25,9,18)(2,24,6,15,5,14)(4,26,12,21,10,19)(7,16,8,17,11,20)(13,22), (1,24,2,14,3,17,4,20,5,23,6,26,7,16,8,19,9,22,10,25,11,15,12,18,13,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 39: $C_{13}:C_3$ 78: $C_{13}:C_6$, 26T5 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 13: None
Low degree siblings
26T15 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
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 $ | $1$ | $1$ | $()$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,18,22,26,17,21,25,16,20,24,15,19, 23)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,22,17,25,20,15,23,18,26,21,16,24, 19)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,20,26,19,25,18,24,17,23,16,22,15, 21)$ |
| $ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $13$ | $(14,25,23,21,19,17,15,26,24,22,20,18,16)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,16,18,20,22,24,26,15,17,19,21,23, 25)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,20,26,19,25,18,24,17,23,16,22,15, 21)$ |
| $ 13, 13 $ | $3$ | $13$ | $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,15,16,17,18,19,20,21,22,23,24,25, 26)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,18,22,26,17,21,25,16,20,24,15,19, 23)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,23,19,15,24,20,16,25,21,17,26,22, 18)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,22,17,25,20,15,23,18,26,21,16,24, 19)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,19,24,16,21,26,18,23,15,20,25,17, 22)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,26,25,24,23,22,21,20,19,18,17,16, 15)$ |
| $ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $13$ | $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)$ |
| $ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $13$ | $(14,23,19,15,24,20,16,25,21,17,26,22,18)$ |
| $ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $13$ | $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,26,25,24,23,22,21,20,19,18,17,16, 15)$ |
| $ 13, 13 $ | $3$ | $13$ | $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,16,18,20,22,24,26,15,17,19,21,23, 25)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,22,17,25,20,15,23,18,26,21,16,24, 19)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,19,24,16,21,26,18,23,15,20,25,17, 22)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,24,21,18,15,25,22,19,16,26,23,20, 17)$ |
| $ 13, 13 $ | $3$ | $13$ | $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,18,22,26,17,21,25,16,20,24,15,19, 23)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,24,21,18,15,25,22,19,16,26,23,20, 17)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,20,26,19,25,18,24,17,23,16,22,15, 21)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,21,15,22,16,23,17,24,18,25,19,26, 20)$ |
| $ 13, 13 $ | $3$ | $13$ | $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,22,17,25,20,15,23,18,26,21,16,24, 19)$ |
| $ 13, 13 $ | $6$ | $13$ | $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,21,15,22,16,23,17,24,18,25,19,26, 20)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1 $ | $169$ | $3$ | $( 2, 4,10)( 3, 7, 6)( 5,13,11)( 8, 9,12)(15,17,23)(16,20,19)(18,26,24) (21,22,25)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1 $ | $169$ | $3$ | $( 2,10, 4)( 3, 6, 7)( 5,11,13)( 8,12, 9)(15,23,17)(16,19,20)(18,24,26) (21,25,22)$ |
| $ 6, 6, 6, 6, 2 $ | $169$ | $6$ | $( 1,23, 3,25, 9,18)( 2,24, 6,15, 5,14)( 4,26,12,21,10,19)( 7,16, 8,17,11,20) (13,22)$ |
| $ 26 $ | $39$ | $26$ | $( 1,15,13,25,12,22,11,19,10,16, 9,26, 8,23, 7,20, 6,17, 5,14, 4,24, 3,21, 2,18 )$ |
| $ 26 $ | $39$ | $26$ | $( 1,19, 9,17, 4,15,12,26, 7,24, 2,22,10,20, 5,18,13,16, 8,14, 3,25,11,23, 6,21 )$ |
| $ 26 $ | $39$ | $26$ | $( 1,18,10,19, 6,20, 2,21,11,22, 7,23, 3,24,12,25, 8,26, 4,14,13,15, 9,16, 5,17 )$ |
| $ 26 $ | $39$ | $26$ | $( 1,21, 7,26,13,18, 6,23,12,15, 5,20,11,25, 4,17,10,22, 3,14, 9,19, 2,24, 8,16 )$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $13$ | $2$ | $( 1,14)( 2,17)( 3,20)( 4,23)( 5,26)( 6,16)( 7,19)( 8,22)( 9,25)(10,15)(11,18) (12,21)(13,24)$ |
| $ 6, 6, 6, 6, 2 $ | $169$ | $6$ | $( 1,17,13,21, 4,18)( 2,26, 9,24, 7,19)( 3,22, 5,14,10,20)( 6,23) ( 8,15,11,16,12,25)$ |
Group invariants
| Order: | $1014=2 \cdot 3 \cdot 13^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [1014, 11] |
| Character table: Data not available. |