Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×#10624391⋊C25 |
| unambiguous semidirect product | (C2×#10624391)⋊C25 |
| derived, Hall | C112⋊C3 ⋊ C22×C25 |
| Hall | (C112⋊C3)⋊C25 ⋊ C22 |
| Hall | #15690027 ⋊ C2×D3 |
| Hall | C2×#10624391 ⋊ C25 |
| Sylow | C112 ⋊ C2×D3×C25 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 208);