Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#4181 |
| Fitting, derived, Hall | C5×C32⋊C9 ⋊ C2 |
| Sylow | C32⋊C9 ⋊ D5 |
| Sylow | C5 ⋊ #4181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊D45 |
| commutator, Fitting, cosocle, hypocenter | C5×C32⋊C9 | C2 |
| Frattini | C32 | C3⋊D15 |
| socle | C32×C5 | C3⋊D3 |
| LCS | G ▷ C5×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
Polycyclic presentation:
2,3^2,5,3^2|b^3=e,b^a=b^2e^2,c^a=c^2,d^a=d^4,e^a=e^2,c^b=cf87 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4181, ((C3⋊D3)⋊C9)⋊D5, #4169⋊D5, … |
| maximal normal subgroup of | D5×#4181, ((C3⋊D3)⋊C9)⋊D5, #4169⋊D5, … |
| maximal quotient of | #13108150, C2×C5⋊#4181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 48);