Finite Group DatabasebetaFinite Group Databasebeta| order | 3300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D55 |
| unambiguous semidirect product | (C5×D3)⋊(C5×D11) |
| Fitting, socle, Hall | C3×C52×C11 ⋊ C22 |
| derived | C3×C5×C11 ⋊ C22×C5 |
| Hall | C52×C11 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D11 |
| Hall | C3×C11 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ D3×D11 |
| Sylow | C11 ⋊ C5×D3×D5 |
| Sylow | C3 ⋊ C2×C5×D55 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D55 |
| commutator, cosocle, hypocenter | C3×C5×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C11 | C22 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
435 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C7×D55, C5×D21×D55, C5×D3×D385, … |
| maximal normal subgroup of | C5×D3×C7×D55, C5×D3×C11×D55 |
| maximal quotient of | C5×D3×C7×D55, C5×D21×D55, C5×D3×D385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3300, 119);