Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#65122 |
| Fitting | C2×C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #11988757, #11988760, #11988778, … |
| maximal normal subgroup of | #11988757, #11988760, #11988778, … |
| maximal quotient of | C2×#10599389, C2×#10599392, C2×Dic5×C4⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12810);