Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $93$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,3,13,2,15)(4,10)(5,11)(6,12)(16,19)(17,21)(18,20), (1,6,7,12,15,17,21,2,5,8,11,13,18,19)(3,4,9,10,14,16,20) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 14: $D_{7}$ 28: $D_{14}$ 84: 21T8 20412: 21T68 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $D_{7}$
Low degree siblings
21T93 x 25, 42T1043 x 26, 42T1044 x 26, 42T1045 x 26, 42T1047 x 13, 42T1048 x 26Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 171 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $61236=2^{2} \cdot 3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |