Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#64886 |
| Sylow | C5 ⋊ C2×#346 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013465, #13013473, #13013593, … |
| maximal normal subgroup of | #13013465, #13013473, #13013593, … |
| maximal quotient of | C2×#10598512, C2×#10598513, #13023022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6783);