Group action invariants
| Degree $n$ : | $27$ | |
| Transitive number $t$ : | $2392$ | |
| Group : | $S_{27}$ | |
| Parity: | $-1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 9: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 3,010 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10888869450418352160768000000=2^{23} \cdot 3^{13} \cdot 5^{6} \cdot 7^{3} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |