Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4062 |
| Fitting | C52×SD16 ⋊ C2 |
| Sylow | C52 ⋊ #135 |
144 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 144 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 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#65736, C5×#65737, #13104622, … |
| maximal normal subgroup of | C5×#65736, C5×#65737, #13104622, … |
| maximal quotient of | C5×#65052, C5×#65076, C5×#65057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 809);