Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D5×#532 |
| Fitting | C5×#532 ⋊ C2 |
| Sylow | C5 ⋊ C2×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Frattini | C22 | C24×D5 |
| Fitting | C5×#532 | C2 |
| hypercenter | #532 | D5 |
| hypocenter | C5 | C2×#532 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1480, D5×#1484, #12065838, … |
| maximal normal subgroup of | D5×#1480, D5×#1484, #12065838, … |
| maximal quotient of | D5×#2285, D5×#2293, D5×#2297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20217);