Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $48$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,2,6,11,9)(3,10,5,7,4)(12,33,17,25,20,29,13,27,22,28)(14,32,16,31,15,26,21,23,18,30)(19,24), (1,25,20)(2,27,18,3,29,16,5,33,12,9,30,15,6,24,21,11,23,22,10,32,13,8,28,17,4,31,14,7,26,19) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5$: $C_5$ $6$: $S_3$ $10$: $C_{10}$ x 3 $12$: $D_{6}$ $20$: 20T3 $30$: $S_3 \times C_5$ $60$: 30T12 $110$: $F_{11}$ $220$: 22T6 $660$: 33T11 $7260$: 33T25 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T48 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 73 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $79860=2^{2} \cdot 3 \cdot 5 \cdot 11^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |