Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic40 |
| Sylow | C52 ⋊ Q32 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
215 conjugacy classes — view the full character table.
| maximal subgroup of | #13099242, #13099244, #13099245, … |
| maximal normal subgroup of | #13099242, #13099244, #13099245, … |
| maximal quotient of | C5×#64724, C5×#64723, C2×C5×Dic40 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 286);