Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $162$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,6,3)(2,4,7)(8,11,12,14,9,13,10)(15,21)(16,19,20,18), (1,14,6,13,4,8,7,10)(2,12,3,11,5,9)(15,21,19)(16,20,18,17), (1,14,15,3,11,16,2,10,17,5,9,19,7,13,18,4,8,21,6,12,20) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ 48: $S_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
42T8089, 42T8090, 42T8091, 42T8092, 42T8093, 42T8094, 42T8095Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 920 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $768144384000=2^{13} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |