Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3968 |
| Sylow | C52 ⋊ #101 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
155 conjugacy classes — view the full character table.
| maximal subgroup of | #13099352, #13099353, #13099354, … |
| maximal normal subgroup of | #13099352, #13099353, #13099354, … |
| maximal quotient of | C5×#64748, C5×#64750, C5×#64763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 321);