Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C4×D5×C22⋊C4 |
| Fitting | C4×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C2×C4×C22⋊C4 |
1360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1282, #11988970, D5×#1284, … |
| maximal normal subgroup of | D5×#1282, #11988970, D5×#1284, … |
| maximal quotient of | C4×D5×#95, C4×#64955, C4×C22⋊C4×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7372);