Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of #4207 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×#4207 |
| Fitting, Hall | C5×#737 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C5 |
| Sylow | #737 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #4207 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C3×C5 |
| Frattini | C3 | C3×C5×C3⋊D3 |
| Fitting | C5×#737 | C2 |
| socle | C3×C5 | C3×C3⋊D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C5 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4207, C5×#4207⋊C2, #4207⋊D5, … |
| maximal normal subgroup of | D5×#4207, C5×#4207⋊C2, #4207⋊D5, … |
| maximal quotient of | C5×#66409, C2×C5×#4207 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 84);