Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3956 |
| Sylow | C52 ⋊ #101 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
155 conjugacy classes — view the full character table.
| maximal subgroup of | #13101156, #13101157, #13101163, … |
| maximal normal subgroup of | #13101156, #13101157, #13101163, … |
| maximal quotient of | C5×#64685, C5×#64689, C5×#64706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 309);