Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
| direct product | SD16×C5⋊D5 |
| Fitting | C52×SD16 ⋊ C2 |
| Sylow | C52 ⋊ C2×SD16 |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#1043, #13104747, SD16×#1044, … |
| maximal normal subgroup of | SD16×#1043, #13104747, SD16×#1044, … |
| maximal quotient of | #13102621, #13102622, #13102623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 892);