Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C37⋊C3×#1043⋊C3 |
| unambiguous semidirect product | (#1043×C37⋊C3)⋊C3 |
| unambiguous semidirect product | (C37×#1043⋊C3)⋊C3 |
| unambiguous semidirect product | (#1043⋊(C37⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C32×C4 |
| Hall | C52⋊C3×C37⋊C3 ⋊ C4 |
| Hall | C37×#1043 ⋊ C32 |
| Hall | #1043 ⋊ C3×C37⋊C3 |
| Sylow | C37 ⋊ C3×#1043⋊C3 |
| Sylow | C52 ⋊ C3×C4×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C32×C4 |
| prime radical | C37⋊C3×(C5⋊D5)⋊C3 | C2 |
| cosocle | C37×C5⋊D5 | C2×C32 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 555 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 431);