Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C3×C37×C22⋊(C52⋊C3) |
| unambiguous semidirect product | (C22×C3)⋊(C37×C52⋊C3) |
| unambiguous semidirect product | (C3×C52)⋊(A4×C37) |
| Fitting, socle | C22×C3×C52×C37 ⋊ C3 |
| derived, Hall | C22×C52 ⋊ C32×C37 |
| Hall | C22×C52×C37 ⋊ C32 |
| Hall | C52×C37 ⋊ C3×A4 |
| Hall | C22×C37 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×A4×C37 |
| Sylow | C22 ⋊ C3×C37×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | C22⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C22×C52 | C32×C37 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52×C37 | C3 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C3×C37 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3330 |
3996 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 775);