Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D5×#518 |
| Fitting | C5×#518 ⋊ C2 |
| Sylow | C5 ⋊ C2×#518 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator | C2×C5 | C24×C4 |
| Fitting | C5×#518 | C2 |
| socle, cosocle | C22×C5 | C25 |
| prime radical | C22×D4×D5 | C2 |
| hypercenter | #518 | D5 |
| hypocenter | C5 | C2×#518 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #518 | |
1920 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1828, D5×#1829, D5×#1856, … |
| maximal normal subgroup of | D5×#1828, D5×#1829, D5×#1856, … |
| maximal quotient of | D5×#2273, D5×#2274, D5×#2275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19849);