Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C3 |
| direct product | C37×C3⋊(C3⋊#1042) |
| unambiguous semidirect product | C3⋊(C37×C3⋊#1042) |
| Fitting, socle, Hall | C32×C52×C37 ⋊ C4 |
| derived, Hall | C32×C52 ⋊ C4×C37 |
| Hall | C52×C37 ⋊ C3⋊Dic3 |
| Hall | C32×C37 ⋊ #1042 |
| Sylow | C52 ⋊ C3⋊Dic3×C37 |
| Sylow | C32 ⋊ C37×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊(C3⋊#1042) |
| commutator, hypocenter | C32×C52 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C4 |
| prime radical | C32×C5×D5×C37 | C2 |
| cosocle | C32×C5×D5 | C2×C37 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C37 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6660 |
3441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 751);