Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | Dic9×C41⋊C25 |
| unambiguous semidirect product | C9⋊(C4×C41⋊C25) |
| unambiguous semidirect product | (Dic9×C41)⋊C25 |
| derived, Hall | C9×C41 ⋊ C4×C25 |
| Hall | C9×C41⋊C25 ⋊ C4 |
| Hall | Dic9×C41 ⋊ C25 |
| Sylow | C41 ⋊ C25×Dic9 |
| Sylow | C9 ⋊ C4×C41⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D9×C41⋊C5 |
| commutator, hypocenter | C9×C41 | C4×C25 |
| Frattini | C2×C3×C5 | D3×C41⋊C5 |
| Fitting, cosocle | C2×C5×C9×C41 | C2×C5 |
| socle, prime radical | C2×C3×C5×C41 | C5×D3 |
| LCS | G ▷ C9×C41 | |
| UCS | C1 ◁ C2×C5 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36900 |
780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 3);