Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic45 |
| derived | C5×C9 ⋊ C4×C9 |
| Hall | C5×C92 ⋊ C4 |
| Sylow | C92 ⋊ Dic5 |
| Sylow | C5 ⋊ C9×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D45 |
| commutator, hypocenter | C5×C9 | C4×C9 |
| Frattini | C2×C32 | C3×D15 |
| Fitting | C2×C5×C92 | C2 |
| socle, prime radical | C2×C32×C5 | C3×D3 |
| cosocle | C2×C3×C5×C9 | C2×C3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2×C9 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 35);