Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $123$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (5,6)(10,11,12)(13,14,15)(17,18)(19,21,20), (1,8,13,21,6,10,18,3,7,14,20,4,11,17)(2,9,15,19,5,12,16) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 7: $C_7$ 14: $C_{14}$ 56: $C_2^3:C_7$ x 2 112: 14T9 x 2 448: 14T21 896: $C_2 \wr C_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7$
Low degree siblings
42T2103 x 6, 42T2104 x 6, 42T2105 x 6, 42T2106 x 6, 42T2107 x 6, 42T2108 x 6, 42T2109 x 6, 42T2110 x 6, 42T2111 x 3, 42T2112 x 6, 42T2113 x 3, 42T2114 x 6, 42T2115 x 6, 42T2116 x 6, 42T2117 x 6, 42T2118 x 6, 42T2119 x 6, 42T2120 x 6, 42T2121 x 6, 42T2122 x 2, 42T2123 x 6, 42T2124, 42T2125 x 2, 42T2126 x 3, 42T2127, 42T2128 x 3, 42T2129, 42T2137 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 333 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1959552=2^{7} \cdot 3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |