Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D5×#538 |
| Fitting | C5×#538 ⋊ C2 |
| Sylow | C5 ⋊ C2×#538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C5×#538 | C2 |
| hypercenter | #538 | D5 |
| hypocenter | C5 | C2×#538 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #538 | |
1336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1600, D5×#1606, D5×#1612, … |
| maximal normal subgroup of | D5×#1600, D5×#1606, D5×#1612, … |
| maximal quotient of | D5×#2312, D5×#2318, D5×#2321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20396);