Group action invariants
| Degree $n$ : | $42$ | |
| Transitive number $t$ : | $46$ | |
| Group : | $C_7\times S_3^2$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,23,2,24,3,22)(4,27,6,26,5,25)(7,30,9,28,8,29)(10,32,11,31,12,33)(13,36,15,35,14,34)(16,39,17,38,18,37)(19,41,21,40,20,42), (1,34,26,16,7,42,32,23,15,6,37,28,19,11,3,36,27,17,8,41,33,24,13,5,38,29,20,12,2,35,25,18,9,40,31,22,14,4,39,30,21,10) | |
| $|\Aut(F/K)|$: | $7$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ x 2 7: $C_7$ 12: $D_{6}$ x 2 36: $S_3^2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$
Degree 3: None
Degree 6: $S_3^2$
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: | $252=2^{2} \cdot 3^{2} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [252, 35] |
| Character table: Data not available. |