Finite Group DatabasebetaFinite Group Databasebeta| order | 16566 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C251 · Schur multiplier (H2) = C1 |
| direct product | D33×C251 |
| unambiguous semidirect product | C3⋊(D11×C251) |
| unambiguous semidirect product | C11⋊(D3×C251) |
| Fitting, socle, Hall | C3×C11×C251 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C251 |
| Hall | C11×C251 ⋊ D3 |
| Hall | C3×C251 ⋊ D11 |
| Sylow | C11 ⋊ D3×C251 |
| Sylow | C3 ⋊ D11×C251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C251 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C251 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C251 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C251 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8283 |
4518 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×D251, D3×D11×C251, D33⋊D251, … |
| maximal normal subgroup of | D33×D251, D3×D11×C251, D33⋊D251, … |
| maximal quotient of | Dic33×C251, C2×D33×C251 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16566, 7);