Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C4×2−1+4⋊C5 |
| unambiguous semidirect product | (C4×2−1+4)⋊C5 |
| Fitting, Sylow | C4×2−1+4 ⋊ C5 |
| derived | 2−1+4 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C24⋊C5 |
| commutator, hypocenter | 2−1+4 | C4×C5 |
| Frattini, socle | C22 | C2×C24⋊C5 |
| Fitting | C4×2−1+4 | C5 |
| prime radical | C2×2−1+4⋊C5 | C2 |
| cosocle | C2×2−1+4 | C2×C5 |
| LCS | G ▷ 2−1+4 | |
| UCS | C1 ◁ C2×C4 | |
169 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | C8×2−1+4⋊C5, C2×C4×2−1+4⋊C5, C4×#585⋊C5, … |
| maximal normal subgroup of | C8×2−1+4⋊C5, C2×C4×2−1+4⋊C5, C4×#585⋊C5, … |
| maximal quotient of | C4×#564⋊C5, C8×2−1+4⋊C5, #60332⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19100);