Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D25 |
| Fitting | Q16×C25 ⋊ C2 |
| Sylow | C25 ⋊ C2×Q16 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #13097894, #13097895, SD32×D25, … |
| maximal normal subgroup of | #13097894, #13097895, SD32×D25, … |
| maximal quotient of | #13098065, #13098067, #13098069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 138);