Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C5×#4057 |
| Fitting | C2×C52×D8 ⋊ C2 |
| Sylow | C52 ⋊ C2×AGL(1,ℤ/8) |
672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9261);