Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×#4169 |
| Fitting, Hall | C5×C32⋊C9 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C5 |
| Sylow | C32⋊C9 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #4169 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C3×C5 |
| Frattini | C32 | C3×C5×D3 |
| Fitting | C5×C32⋊C9 | C2 |
| socle | C32×C5 | C3×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C5 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4169, C5×((C3⋊D3)⋊C9)⋊C2, #4169⋊D5, … |
| maximal normal subgroup of | D5×#4169, C5×((C3⋊D3)⋊C9)⋊C2, #4169⋊D5, … |
| maximal quotient of | C5×#66316, C2×C5×#4169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 16);