Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $87$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,14,2,16,9)(3,21,11,7,20,12)(4,19,13,6,15,10)(5,17,8), (1,17,7,16,4,20,2,18,3,19,6,15)(5,21)(8,11,10)(9,13,14), (1,21,13,7,20,9,6,19,12,5,18,8,4,17,11,3,16,14,2,15,10) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $S_3$, $C_6$ x 3 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $S_4$ 36: $C_6\times S_3$ 48: $S_4\times C_2$ 72: 12T45 144: 18T61 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
28T544, 42T991, 42T992, 42T993, 42T994, 42T995, 42T996, 42T997, 42T998Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 51 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $49392=2^{4} \cdot 3^{2} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |