Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#66108 |
| Fitting | C52×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C52 ⋊ #576 |
604 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #72220868, C5×#10619093, #72221385, … |
| maximal normal subgroup of | #72220868, C5×#10619093, #72221385, … |
| maximal quotient of | C5×#10612596 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9280);