Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#64774 |
| Sylow | C5 ⋊ C2×#343 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×#343, C4×#64774, #12004566, … |
| maximal normal subgroup of | Dic5×#343, C4×#64774, #12004566, … |
| maximal quotient of | C2×#10598165, #11988896, #11988899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4861);