Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D5×#560 |
| Fitting | C5×#560 ⋊ C2 |
| Sylow | C5 ⋊ C2×#560 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C5×#560 | C2 |
| hypercenter | #560 | D5 |
| hypocenter | C5 | C2×#560 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #560 | |
1344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2200, C2×D5×#560, D5×#3529, … |
| maximal normal subgroup of | D5×#2200, C2×D5×#560, D5×#3529, … |
| maximal quotient of | D5×#2375, D5×#2376, D5×#2377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21062);