Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C22⋊C4×D25 |
| Fitting | C22⋊C4×C25 ⋊ C2 |
| Sylow | C25 ⋊ C2×C22⋊C4 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13097853, #99×D25, C22⋊C4×#1035, … |
| maximal normal subgroup of | #13097853, #99×D25, C22⋊C4×#1035, … |
| maximal quotient of | #13097921, #13097922, #13097923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 101);