Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D9 |
| Fitting, Hall | C32×C5×C9 ⋊ C2 |
| derived | C9 ⋊ C2×C32×C5 |
| Sylow | C32×C9 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C32×C5 |
| Frattini | C3 | C32×C5×D3 |
| Fitting | C32×C5×C9 | C2 |
| socle | C33×C5 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C32×C5 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 270 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×D9, C3×C5×D3×D9, C3×D9×D15, … |
| maximal normal subgroup of | C32×D5×D9, C3×C5×D3×D9, C3×D9×D15, … |
| maximal quotient of | C32×C5×Dic9, C2×C32×C5×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 67);