Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $144$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,8,3,15,7,2,14,9)(4,18)(5,17)(6,16)(10,11,12)(19,21,20), (1,6,12,18,7,20,3,4,11,17,9,19,2,5,10,16,8,21)(13,15) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 5040: $S_7$ 10080: $S_7\times C_2$ 30240: 21T74 7348320: 21T138 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $S_7$
Low degree siblings
21T144, 42T2921 x 2, 42T2922 x 2, 42T2923 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 261 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $22044960=2^{5} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |