Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic5×D20 |
| Sylow | C52 ⋊ C4×D4 |
214 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 214 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) = 160 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #13099750, #13099751, #13100606, … |
| maximal normal subgroup of | #13099750, #13099751, #13100606, … |
| maximal quotient of | #168×D20, #13100505, #13100517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 671);