Finite Group DatabasebetaFinite Group Databasebeta| order | 6666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D303 |
| unambiguous semidirect product | C3⋊(C11×D101) |
| unambiguous semidirect product | C101⋊(D3×C11) |
| Fitting, socle, Hall | C3×C11×C101 ⋊ C2 |
| derived, Hall | C3×C101 ⋊ C2×C11 |
| Hall | C11×C101 ⋊ D3 |
| Sylow | C101 ⋊ D3×C11 |
| Hall | C3×C11 ⋊ D101 |
| Sylow | C3 ⋊ C11×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D303 |
| commutator, hypocenter | C3×C101 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C101 | C2 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
1683 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×D101, D11×D303, D33⋊D101, … |
| maximal normal subgroup of | D3×C11×D101, D11×D303, D33⋊D101, … |
| maximal quotient of | C11×Dic303, C2×C11×D303, C11×D909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6666, 6);