Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#65980 |
| Fitting | C2×C5×C22⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#563 |
1024 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
94 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#65980, #12262012, #12265160, … |
| maximal normal subgroup of | C4×#65980, #12262012, #12265160, … |
| maximal quotient of | C2×#10605744, C2×#10606329, C2×#10608348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19955);