Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3958 |
| Fitting | C52×D8 ⋊ C2 |
| Sylow | C52 ⋊ D16 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3958, #13101205, #13101206, … |
| maximal normal subgroup of | D5×#3958, #13101205, #13101206, … |
| maximal quotient of | C5×#64709, C5×#64711, C5×#64739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 311);