Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5 |
| direct product | C52⋊C3×#3866⋊C3 |
| unambiguous semidirect product | (C52×#3866⋊C3)⋊C3 |
| unambiguous semidirect product | (#3866⋊(C52⋊C3))⋊C3 |
| unambiguous semidirect product | (C52⋊C3×#3866)⋊C3 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C32×C4 |
| Hall | C52⋊C3×C37⋊C3 ⋊ C4 |
| Hall | C52×#3866 ⋊ C32 |
| Hall | #3866 ⋊ C3×C52⋊C3 |
| Sylow | C37 ⋊ C3×C4×C52⋊C3 |
| Sylow | C52 ⋊ C3×#3866⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C32×C4 |
| prime radical | C52⋊C3×D37⋊C3 | C2 |
| cosocle | C52×D37 | C2×C32 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 555 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 414);