Group action invariants
| Degree $n$ : | $42$ | |
| Transitive number $t$ : | $24$ | |
| Group : | $C_{14}\times A_4$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,27,39,8,19,34)(2,17,28,40,7,20,33)(3,14,29,41,10,21,36)(4,13,30,42,9,22,35)(5,16,26,38,11,23,31,6,15,25,37,12,24,32), (1,5,3)(2,6,4)(7,12,9)(8,11,10)(13,17,16)(14,18,15)(19,24,21)(20,23,22)(25,30,28)(26,29,27)(31,36,34)(32,35,33)(37,41,39)(38,42,40) | |
| $|\Aut(F/K)|$: | $14$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 7: $C_7$ 12: $A_4$ 24: $A_4\times C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: $A_4\times C_2$
Degree 7: $C_7$
Degree 14: None
Degree 21: $C_{21}$
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 56 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $168=2^{3} \cdot 3 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [168, 52] |
| Character table: Data not available. |