Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65294 |
| Fitting | C2×C5×#117 ⋊ C2 |
| Sylow | C5 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12004761, #12004763, #12004768, … |
| maximal normal subgroup of | #12004761, #12004763, #12004768, … |
| maximal quotient of | C2×#10601550, C2×#10601560, C2×#10601548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16034);