Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#64894 |
| Fitting | C22×C5×C8 ⋊ C4 |
| Sylow | C5 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#64894, #13021623, #13021628, … |
| maximal normal subgroup of | C4×#64894, #13021623, #13021628, … |
| maximal quotient of | C2×#10598774, #13015567, #13015571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6807);