Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of C9⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C9 |
| direct product | C5×C9⋊D9 |
| unambiguous semidirect product | C9⋊(C5×D9) |
| Fitting, Hall | C5×C92 ⋊ C2 |
| derived, Sylow | C92 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C9⋊D9 |
| commutator, cosocle, hypocenter | C92 | C2×C5 |
| Frattini | C32 | C5×C3⋊D3 |
| Fitting | C5×C92 | C2 |
| socle | C32×C5 | C3⋊D3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C5 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 405 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#66343, #13108196, D5×C9⋊D9, … |
| maximal normal subgroup of | C5×#66343, #13108196, D5×C9⋊D9, … |
| maximal quotient of | C5×C9⋊Dic9, C2×C5×C9⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 40);