Group action invariants
| Degree $n$ : | $14$ | |
| Transitive number $t$ : | $52$ | |
| CHM label : | $[L(7)^{2}]2=L(7)wr2$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (2,4,6,8,10,12,14), (2,4)(6,12), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14), (2,4,8)(6,12,10) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 7: None
Low degree siblings
14T52, 16T1861, 28T546 x 2, 42T1003Siblings 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 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $441$ | $2$ | $( 2,12)( 4, 6)( 5, 9)(11,13)$ |
| $ 4, 4, 2, 2, 1, 1 $ | $1764$ | $4$ | $( 2, 4)( 3, 5, 7,13)( 6,10,12,14)( 9,11)$ |
| $ 3, 3, 3, 3, 1, 1 $ | $3136$ | $3$ | $( 2,10,12)( 3, 5, 9)( 4,14, 6)( 7,13,11)$ |
| $ 7, 7 $ | $576$ | $7$ | $( 1, 3, 5, 7, 9,11,13)( 2, 4, 6, 8,10,12,14)$ |
| $ 7, 7 $ | $576$ | $7$ | $( 1, 3, 5,13,11, 7, 9)( 2, 8,10,12, 6, 4,14)$ |
| $ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $42$ | $2$ | $( 2,12)( 4, 6)$ |
| $ 4, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $84$ | $4$ | $( 2, 4)( 6,10,12,14)$ |
| $ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $112$ | $3$ | $( 2,10,12)( 4,14, 6)$ |
| $ 7, 1, 1, 1, 1, 1, 1, 1 $ | $48$ | $7$ | $( 2, 4, 6, 8,10,12,14)$ |
| $ 7, 1, 1, 1, 1, 1, 1, 1 $ | $48$ | $7$ | $( 2, 8,10,12, 6, 4,14)$ |
| $ 4, 2, 2, 2, 1, 1, 1, 1 $ | $1764$ | $4$ | $( 2, 4)( 5, 9)( 6,10,12,14)(11,13)$ |
| $ 3, 3, 2, 2, 1, 1, 1, 1 $ | $2352$ | $6$ | $( 2,10,12)( 4,14, 6)( 5, 9)(11,13)$ |
| $ 7, 2, 2, 1, 1, 1 $ | $1008$ | $14$ | $( 2, 4, 6, 8,10,12,14)( 5, 9)(11,13)$ |
| $ 7, 2, 2, 1, 1, 1 $ | $1008$ | $14$ | $( 2, 8,10,12, 6, 4,14)( 5, 9)(11,13)$ |
| $ 4, 3, 3, 2, 1, 1 $ | $4704$ | $12$ | $( 2,10,12)( 3, 5, 7,13)( 4,14, 6)( 9,11)$ |
| $ 7, 4, 2, 1 $ | $2016$ | $28$ | $( 2, 4, 6, 8,10,12,14)( 3, 5, 7,13)( 9,11)$ |
| $ 7, 4, 2, 1 $ | $2016$ | $28$ | $( 2, 8,10,12, 6, 4,14)( 3, 5, 7,13)( 9,11)$ |
| $ 7, 3, 3, 1 $ | $2688$ | $21$ | $( 2, 4, 6, 8,10,12,14)( 3, 5, 9)( 7,13,11)$ |
| $ 7, 3, 3, 1 $ | $2688$ | $21$ | $( 2, 8,10,12, 6, 4,14)( 3, 5, 9)( 7,13,11)$ |
| $ 7, 7 $ | $1152$ | $7$ | $( 1, 3, 5, 7, 9,11,13)( 2, 8,10,12, 6, 4,14)$ |
| $ 2, 2, 2, 2, 2, 2, 2 $ | $168$ | $2$ | $( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)$ |
| $ 4, 4, 2, 2, 2 $ | $3528$ | $4$ | $( 1, 8)( 2, 9,12, 5)( 3,10)( 4,11, 6,13)( 7,14)$ |
| $ 14 $ | $4032$ | $14$ | $( 1,10, 3,12, 5,14, 7, 2, 9, 4,11, 6,13, 8)$ |
| $ 14 $ | $4032$ | $14$ | $( 1,10, 3,12, 5, 6,13, 4,11,14, 7, 2, 9, 8)$ |
| $ 8, 4, 2 $ | $7056$ | $8$ | $( 1, 8)( 2, 9, 4,11)( 3,12, 5,14, 7, 6,13,10)$ |
| $ 6, 6, 2 $ | $9408$ | $6$ | $( 1, 8)( 2, 9,10, 3,12, 5)( 4,11,14, 7, 6,13)$ |
Group invariants
| Order: | $56448=2^{7} \cdot 3^{2} \cdot 7^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |