Finite Group DatabasebetaFinite Group Databasebeta| order | 3300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×D11×C52⋊C3 |
| unambiguous semidirect product | C11⋊(C22×C52⋊C3) |
| unambiguous semidirect product | (C2×C11)⋊(C2×C52⋊C3) |
| unambiguous semidirect product | (C2×C52×D11)⋊C3 |
| Fitting, socle | C2×C52×C11 ⋊ C2×C3 |
| derived, Hall | C52×C11 ⋊ C22×C3 |
| Hall | C2×C52×D11 ⋊ C3 |
| Hall | C11×C52⋊C3 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ C22×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D11×C52⋊C3 |
| commutator, cosocle, hypocenter | C52×C11 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C11 | C2×C3 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3300, 98);