Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D3×C25×D123 |
| unambiguous semidirect product | (C3×D3)⋊(C25×D41) |
| Fitting, Hall | C32×C25×C41 ⋊ C22 |
| derived, Hall | C32×C41 ⋊ C22×C25 |
| Hall | C25×C41 ⋊ D32 |
| Hall | C32×C25 ⋊ C2×D41 |
| Sylow | C41 ⋊ D32×C25 |
| Sylow | C32 ⋊ C2×C25×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D3×D123 |
| commutator, hypocenter | C32×C41 | C22×C25 |
| Frattini | C5 | C5×D3×D123 |
| Fitting | C32×C25×C41 | C22 |
| socle, cosocle | C32×C5×C41 | C22×C5 |
| prime radical | C5×D3×D123 | C5 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C25 | |
132 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6150 |
4725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 144);