Group action invariants
| Degree $n$: | $21$ | |
| Transitive number $t$: | $40$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,6,2)(4,5,7)(8,21,11,20,9,16)(10,18,12,15,13,17)(14,19), (1,19,8,2,15,11,3,18,14,4,21,10,5,17,13,6,20,9,7,16,12) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $S_3$, $C_6$ $18$: $S_3\times C_3$ $21$: $C_7:C_3$ $42$: $(C_7:C_3) \times C_2$ $126$: 21T11 $882$: 14T26 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
21T40 x 5, 42T464 x 6, 42T473 x 3, 42T474 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 60 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $6174=2 \cdot 3^{2} \cdot 7^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |