Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C22×#4022 |
| Fitting | C22×C42×C5 ⋊ C2 |
| Sylow | C5 ⋊ C22×#126 |
1320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #11990662, #12023822, #12023826, … |
| maximal normal subgroup of | #11990662, #12023822, #12023826, … |
| maximal quotient of | C22×#65226, C22×#65222, C22×#65229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19659);