Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | #1044×#66526 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C4×C9 |
| Hall | C52×#66526 ⋊ C4 |
| Hall | C37×#1044 ⋊ C9 |
| Sylow | C37 ⋊ C9×#1044 |
| Sylow | C52 ⋊ C4×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C4×C9 |
| prime radical, cosocle | C5⋊D5×C37⋊C3 | C2×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 370 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 457);