Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1023$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,17,3,14,19)(2,8,18,4,13,20)(5,11)(6,12)(9,16)(10,15), (1,4,2,3)(5,20,14,7,6,19,13,8)(9,11,17,15,10,12,18,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 7200: $A_5 \wr C_2$ 14400: 20T458 28800: 20T546 1843200: 20T985 3686400: 20T1008 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $A_5 \wr C_2$
Low degree siblings
20T1023, 40T171489 x 2, 40T171490 x 2, 40T171504, 40T171537 x 2, 40T171538 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 324 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $7372800=2^{15} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |