Group action invariants
| Degree $n$: | $21$ | |
| Transitive number $t$: | $31$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,16,11,4,19,9)(2,17,8,3,18,12)(5,20,13,7,15,14)(6,21,10), (1,12,19,6,11,21,4,10,16,2,9,18,7,8,20,5,14,15,3,13,17) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $C_6$ $14$: $D_{7}$ $42$: $F_7$ x 2, 21T3 $294$: 21T16 x 2, 21T19 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
21T31 x 11, 42T268 x 12Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 71 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2058=2 \cdot 3 \cdot 7^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |