Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D5⋊M16 |
| unambiguous semidirect product | D5⋊(C5×M16) |
| Sylow | C52 ⋊ C2×M16 |
144 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #13099782, #13099783, #13099788, … |
| maximal normal subgroup of | #13099782, #13099783, #13099788, … |
| maximal quotient of | C5×#65676, C4×C5×#700, C5×D5⋊(C4⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1068);