Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $102$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,3,2,4,7)(8,18,11,15,9,17)(10,16,12,21,13,20)(14,19), (1,21,12,2,19,13,5,20,9,7,16,11,6,18,10,3,17,14)(4,15,8) | |
| $|\Aut(F/K)|$: | $1$ |
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: $S_3\times C_3$ 36: $C_6\times S_3$ 54: $C_3^2 : C_6$ 108: 18T41 162: $C_3 \wr S_3 $ 324: 18T119 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
42T1255, 42T1256, 42T1257Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 70 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $111132=2^{2} \cdot 3^{4} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |