Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65015 |
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#407 |
1008 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #11988898, #11988904, #11988910, … |
| maximal normal subgroup of | #11988898, #11988904, #11988910, … |
| maximal quotient of | C2×#10598913, C2×#10598937, C2×#10598895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12411);