Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D9×C5⋊(D41⋊C5) |
| unambiguous semidirect product | (C5×D9)⋊(D41⋊C5) |
| unambiguous semidirect product | (D9×C41⋊C5)⋊D5 |
| unambiguous semidirect product | (D9×D205)⋊C5 |
| Fitting, derived | C5×C9×C41 ⋊ C22×C5 |
| Hall | C5×C9×C41⋊C5 ⋊ C22 |
| Hall | C5×C41⋊C5 ⋊ C2×D9 |
| Hall | C9×C41 ⋊ C2×C5×D5 |
| Sylow | C41 ⋊ C5×D5×D9 |
| Sylow | C9 ⋊ C2×C5⋊(D41⋊C5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C41 | C22×C5 |
| Frattini | C3 | D3×C5⋊(D41⋊C5) |
| socle | C3×C5×C41 | C2×C5×D3 |
| LCS | G ▷ C5×C9×C41 | |
| UCS | C1 | |
144 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1845 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 192);