Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#65417 |
| Fitting | C22×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#436 |
552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12017473, #12097634, #12097637, … |
| maximal normal subgroup of | #12017473, #12097634, #12097637, … |
| maximal quotient of | C2×#10601652, C2×#10601659, C2×#10601743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17568);