Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×#66526⋊C2 |
| unambiguous semidirect product | #66526⋊(C22×C52) |
| unambiguous semidirect product | (C2×#66526)⋊(C2×C52) |
| Fitting, socle | C2×C52×C37 ⋊ C2×C9 |
| derived, Sylow | C37 ⋊ C22×C52×C9 |
| Hall | C52×#66526 ⋊ C22 |
| Hall | C2×C52×D37 ⋊ C9 |
| Hall | C52×C37 ⋊ C22×C9 |
| Hall | #66526 ⋊ C22×C52 |
| Hall | C2×D37 ⋊ C52×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | #66526⋊C2 |
| commutator, hypocenter | C37 | C22×C52×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C37 | C2×C9 |
| prime radical | C2×C52×D37⋊C3 | C3 |
| cosocle | C37⋊C3 | C22×C3×C52 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C52 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1850 |
1000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 466);