Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#64988 |
| Sylow | C5 ⋊ C2×#494 |
552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | #11994605, #11998539, #11998541, … |
| maximal normal subgroup of | #11994605, #11998539, #11998541, … |
| maximal quotient of | C2×#10598856, C2×#10598857, C2×#10598858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12287);