Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C32×C52×#3866 |
| Fitting, socle, Hall | C32×C52×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C32×C4×C52 |
| Hall | C52×C37 ⋊ C32×C4 |
| Hall | C32×C37 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C52 | #3866 |
| commutator, hypocenter | C37 | C32×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C4 |
| prime radical | C32×C52×D37 | C2 |
| cosocle | D37 | C2×C32×C52 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32×C52 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
2925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 656);