Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#65434 |
| Fitting | C2×C5×#131 ⋊ C2 |
| Sylow | C5 ⋊ C2×#444 |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12016206, #12016207, #12016209, … |
| maximal normal subgroup of | #12016206, #12016207, #12016209, … |
| maximal quotient of | C2×#10601730, C2×#10601632, C2×#10601725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17604);