Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C37 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C37×C5⋊D45 |
| unambiguous semidirect product | (C2×C5)⋊(C37×D45) |
| unambiguous semidirect product | (C2×C9)⋊(C37×C5⋊D5) |
| Fitting | C2×C52×C9×C37 ⋊ C2 |
| derived, Hall | C52×C9 ⋊ C22×C37 |
| Hall | C52×C9×C37 ⋊ C22 |
| Hall | C52×C37 ⋊ C2×D9 |
| Hall | C9×C37 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D9×C37 |
| Sylow | C9 ⋊ C2×C37×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | C5⋊D45 |
| commutator, cosocle, hypocenter | C52×C9 | C22×C37 |
| Frattini | C3 | C2×C37×C3⋊(C5⋊D5) |
| Fitting | C2×C52×C9×C37 | C2 |
| socle | C2×C3×C52×C37 | D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C2×C37 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16650 |
8436 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 336);