Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×(C3⋊D3)⋊D31 |
| unambiguous semidirect product | (C3⋊D3)⋊(C25×D31) |
| Fitting, Hall | C32×C25×C31 ⋊ C22 |
| derived, Hall | C32×C31 ⋊ C22×C25 |
| Hall | C25×C31 ⋊ D32 |
| Hall | C32×C25 ⋊ C2×D31 |
| Sylow | C31 ⋊ D32×C25 |
| Sylow | C32 ⋊ C2×C25×D31 |
132 conjugacy classes of subgroups.
2475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 188);