Group action invariants
| Degree $n$ : | $42$ | |
| Transitive number $t$ : | $20$ | |
| Group : | $C_{21}\times S_3$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (4,5,6)(10,12,11)(16,18,17)(22,24,23)(28,30,29)(34,35,36)(40,41,42), (1,5,7,12,13,18,21,22,26,29,33,34,37,40,3,6,8,11,14,17,19,24,27,28,31,35,38,41,2,4,9,10,15,16,20,23,25,30,32,36,39,42) | |
| $|\Aut(F/K)|$: | $21$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $S_3$, $C_6$ 7: $C_7$ 18: $S_3\times C_3$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$
Degree 3: None
Degree 6: $S_3\times C_3$
Degree 7: $C_7$
Degree 14: $C_{14}$
Degree 21: None
Low degree siblings
There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.
Conjugacy Classes
There are 63 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $126=2 \cdot 3^{2} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [126, 12] |
| Character table: Data not available. |