Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#64899 |
| Fitting | C2×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ C2×#343 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#343, C4×#64899, #13021675, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#343, C4×#64899, #13021675, … |
| maximal quotient of | C2×#10598551, #13015530, #13015533, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6841);