Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#87872 |
| Sylow | C52 ⋊ C22×Q8 |
366 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | #13100782, #13100783, #13100786, … |
| maximal normal subgroup of | #13100782, #13100783, #13100786, … |
| maximal quotient of | #13104943, #13104945, C4×#87872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1123);