Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | D5×#733 |
| unambiguous semidirect product | C5⋊(C2×#733) |
| Fitting, Hall | C5×#733 ⋊ C2 |
| Sylow | C5 ⋊ C2×#733 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#733, #733⋊AGL(1,𝔽5), D5×#733⋊C2, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#733, #733⋊AGL(1,𝔽5), D5×#733⋊C2, … |
| maximal quotient of | Dic5×#733, C2×D5×#733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 13);