Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | D5×#731 |
| unambiguous semidirect product | C5⋊(C2×#731) |
| Fitting, Hall | C5×#731 ⋊ C2 |
| Sylow | C5 ⋊ C2×#731 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#731, #13108184, #13108185, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#731, #13108184, #13108185, … |
| maximal quotient of | Dic5×#731, C2×D5×#731 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 11);