Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×C22⋊#66526 |
| unambiguous semidirect product | C22⋊(C52×#66526) |
| unambiguous semidirect product | (C22×C5)⋊(C5×#66526) |
| Fitting, socle, Hall | C22×C52×C37 ⋊ C9 |
| derived, Hall | C22×C37 ⋊ C52×C9 |
| Hall | C52×C37 ⋊ C22⋊C9 |
| Hall | C22×C52 ⋊ #66526 |
| Sylow | C37 ⋊ C52×C22⋊C9 |
| Sylow | C22 ⋊ C52×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C22⋊#66526 |
| commutator, hypocenter | C22×C37 | C52×C9 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C37 | C9 |
| prime radical | C22×C52×C37⋊C3 | C3 |
| cosocle | C22×C37⋊C3 | C3×C52 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C52 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3700 |
700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 598);