Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×#20301658 |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C4 |
| derived | C32×C5×C41 ⋊ C4×C5 |
| Hall | C52×C41 ⋊ #157 |
| Hall | C32×C41 ⋊ C5×Dic5 |
| Hall | C32×C52 ⋊ Dic41 |
| Sylow | C41 ⋊ C5×#4379 |
| Sylow | C52 ⋊ #13093288 |
| Sylow | C32 ⋊ C5×Dic205 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20301658 |
| commutator, hypocenter | C32×C5×C41 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C41 | C4 |
| prime radical | C52×C3⋊D3×C41 | C2 |
| cosocle | C5×C3⋊D3×C41 | C2×C5 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 ◁ C5 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1230 |
3090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 464);