Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $145$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,3,9)(2,8)(4,11,17,13,6,10,16,15)(5,12,18,14)(19,20,21), (1,10,18,5,9,19,14,3,11,17,6,8,20,15,2,12,16,4,7,21,13) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 168: $\GL(3,2)$ 1344: $C_2^3:\GL(3,2)$ 10752: 14T50 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
42T2982, 42T2983, 42T2984, 42T2986Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 132 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $23514624=2^{9} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |