Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#65411 |
| Sylow | C5 ⋊ C2×#405 |
592 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12004468, #12004470, #12004491, … |
| maximal normal subgroup of | #12004468, #12004470, #12004491, … |
| maximal quotient of | C2×M16×#168, C2×#10601533, C2×#10600640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17559);