Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $53$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,4,13,2,11,3,14)(5,7,21,19,6,8,22,20)(9,17)(10,18)(15,16), (1,11,5,4,22,17,20,9)(2,12,6,3,21,18,19,10)(7,16,8,15)(13,14), (1,12,4,20,17,14)(2,11,3,19,18,13)(5,15,8,21,6,16,7,22) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 39916800: $S_{11}$ 79833600: 22T47 40874803200: 22T50 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $S_{11}$
Low degree siblings
22T53, 44T1774, 44T1777 x 2, 44T1778 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 752 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $81749606400=2^{19} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |