Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#3966 |
| Sylow | C52 ⋊ #99 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
155 conjugacy classes — view the full character table.
| maximal subgroup of | #13099342, #13099344, #13099345, … |
| maximal normal subgroup of | #13099342, #13099344, #13099345, … |
| maximal quotient of | C5×#64745, C5×#64746, C5×#64748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 319);