Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#4082 |
| Sylow | C52 ⋊ #124 |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13099350, C5×#64693, C5×#64921, … |
| maximal normal subgroup of | #13099350, C5×#64693, C5×#64921, … |
| maximal quotient of | C5×#65234, C5×#65236, C5×#65242, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 829);