Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | A4×C52⋊(C37⋊C3) |
| unambiguous semidirect product | (C52×A4)⋊(C37⋊C3) |
| unambiguous semidirect product | (A4×C37)⋊(C52⋊C3) |
| Fitting, socle, derived, Hall | C22×C52×C37 ⋊ C32 |
| Hall | C52×C37 ⋊ C3×A4 |
| Hall | C22×C37 ⋊ C3×C52⋊C3 |
| Hall | C22×C52 ⋊ C3×C37⋊C3 |
| Sylow | C37 ⋊ A4×C52⋊C3 |
| Sylow | C52 ⋊ A4×C37⋊C3 |
| Sylow | C22 ⋊ C3×C52⋊(C37⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C52×C37 | C32 |
| LCS | G ▷ C22×C52×C37 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2220 |
1244 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 596);