Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
| direct product | Q32×C5⋊D5 |
| Fitting | C52×Q32 ⋊ C2 |
| Sylow | C52 ⋊ C2×Q32 |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5132);