Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#11717425 |
| unambiguous semidirect product | D5⋊#4072 |
| Fitting | C22×C4×C52 ⋊ C4 |
| Sylow | C52 ⋊ C2×#117 |
687 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10136);