Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#4027 |
| Fitting | C52×C22⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ C4×D4 |
222 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#65692, C5×#65693, C5×#65694, … |
| maximal normal subgroup of | C5×#65692, C5×#65693, C5×#65694, … |
| maximal quotient of | C5×#64955, C5×#64938, C5×#64936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 774);