Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D80 |
| Fitting | C52×C16 ⋊ C2 |
| Sylow | C52 ⋊ D16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
215 conjugacy classes — view the full character table.
| maximal subgroup of | #13099240, #13099241, #13099242, … |
| maximal normal subgroup of | #13099240, #13099241, #13099242, … |
| maximal quotient of | C5×#64669, C5×D160, C5×Dic80, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 284);