Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D5×#556 |
| Fitting | C5×#556 ⋊ C2 |
| Sylow | C5 ⋊ C2×#556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C5×#556 | C2 |
| prime radical | C2×D4×D5 | C22 |
| hypercenter | #556 | D5 |
| hypocenter | C5 | C2×#556 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #556 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1628, D5×#1638, D5×#1652, … |
| maximal normal subgroup of | D5×#1628, D5×#1638, D5×#1652, … |
| maximal quotient of | D5×#2347, D5×#2354, D5×#2355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20986);