Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#4076 |
| Fitting | C22×C42×C5 ⋊ C2 |
| Sylow | C5 ⋊ C4×#121 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #11987257, #11987260, #11987330, … |
| maximal normal subgroup of | #11987257, #11987260, #11987330, … |
| maximal quotient of | C4×#65502, C4×#65229, C4×#65228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15884);