Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#30659275 |
| Fitting, socle | C2×C52×C37 ⋊ C2×C9 |
| derived, Hall | C52×C37 ⋊ C22×C9 |
| Hall | C52⋊#66526 ⋊ C22 |
| Hall | C2×C52×D37 ⋊ C9 |
| Hall | C2×D37 ⋊ C52⋊C9 |
| Sylow | C37 ⋊ C22×C52⋊C9 |
| Sylow | C52 ⋊ C2×#66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30659275 |
| commutator, hypocenter | C52×C37 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C37 | C2×C9 |
| prime radical | C2×C52×D37⋊C3 | C3 |
| cosocle | C52×C37⋊C3 | C22×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1110 |
232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 458);