Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| direct product | D5×C32⋊C9 |
| unambiguous semidirect product | C5⋊(C2×C32⋊C9) |
| unambiguous semidirect product | (C32×D5)⋊C9 |
| Fitting, Hall | C5×C32⋊C9 ⋊ C2 |
| Sylow | C5 ⋊ C2×C32⋊C9 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×C32⋊C9, (C3⋊ΓL(1,𝔽16))⋊C9, #13108177, … |
| maximal normal subgroup of | AGL(1,𝔽5)×C32⋊C9, (C3⋊ΓL(1,𝔽16))⋊C9, #13108177, … |
| maximal quotient of | Dic5×C32⋊C9, C2×D5×C32⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 6);