Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#65224 |
| Sylow | C5 ⋊ C2×#384 |
888 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598193, #11989394, #11989404, … |
| maximal normal subgroup of | C2×#10598193, #11989394, #11989404, … |
| maximal quotient of | C2×#10602328, C4×#65224, C2×#10600212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15874);