Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3939 |
| Sylow | C52 ⋊ #107 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13100592, #13100594, #13100596, … |
| maximal normal subgroup of | #13100592, #13100594, #13100596, … |
| maximal quotient of | C5×#64699, C5×#64709, C5×#64710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 292);