Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D3×C41⋊C25 |
| unambiguous semidirect product | (C2×C3)⋊(D3×C41⋊C25) |
| unambiguous semidirect product | (C2×C3⋊D3×C41)⋊C25 |
| derived, Hall | C32×C41 ⋊ C22×C25 |
| Hall | C32×C41⋊C25 ⋊ C22 |
| Hall | C2×C3⋊D3×C41 ⋊ C25 |
| Sylow | C41 ⋊ C2×C3⋊D3×C25 |
| Sylow | C32 ⋊ C22×C41⋊C25 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18450 |
780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 110);