Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D5×#564 |
| Fitting | C5×#564 ⋊ C2 |
| Sylow | C5 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C5×#564 | C2 |
| prime radical | C22×D5 | C24 |
| hypercenter | #564 | D5 |
| hypocenter | C5 | C2×#564 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #564 | |
896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1658, D5×#1663, #12080600, … |
| maximal normal subgroup of | D5×#1658, D5×#1663, #12080600, … |
| maximal quotient of | D5×#2382, #12262020, Dic5×#564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21125);