Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4057 |
| Fitting | C52×D8 ⋊ C2 |
| Sylow | C52 ⋊ AGL(1,ℤ/8) |
158 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4057, #13105817, #13105819, … |
| maximal normal subgroup of | D5×#4057, #13105817, #13105819, … |
| maximal quotient of | C5×#65050, C5×#65051, C5×#65052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 804);