Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | #4223×C52⋊C9 |
| unambiguous semidirect product | (C52×#4223)⋊C9 |
| derived, Hall | C52×C41 ⋊ C4×C9 |
| Hall | C41×C52⋊C9 ⋊ C4 |
| Hall | C52×#4223 ⋊ C9 |
| Sylow | C41 ⋊ C4×C52⋊C9 |
| Sylow | C52 ⋊ C9×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊C3×#4223 |
| commutator, hypocenter | C52×C41 | C4×C9 |
| Fitting, socle | C3×C52×C41 | C3×C4 |
| prime radical, cosocle | C3×C52×D41 | C2×C3 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 210);