Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×Dic5 |
| derived, Sylow | C5 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D5 |
| commutator, hypocenter | C5 | C23×C42 |
| Frattini | C22 | C24×D5 |
| Fitting | C24×C4×C5 | C2 |
| socle, prime radical | C25×C5 | C22 |
| cosocle | C22×C5 | C25 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C4 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #11987219, #12004517, #12004541, … |
| maximal normal subgroup of | #11987219, #12004517, #12004541, … |
| maximal quotient of | C22×C42×Dic5, C23×#3963, C22×#65221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21197);