Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×C8×D5 |
| Fitting | C23×C5×C8 ⋊ C2 |
| derived, Sylow | C5 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D5 |
| commutator, hypocenter | C5 | C24×C8 |
| Frattini | C4 | C24×D5 |
| Fitting | C23×C5×C8 | C2 |
| socle | C24×C5 | C2×C4 |
| prime radical | C24×D5 | C4 |
| cosocle | C4×C5 | C25 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #12004522, #12004548, #12004554, … |
| maximal normal subgroup of | #12004522, #12004548, #12004554, … |
| maximal quotient of | C22×C4×C8×D5, C23×C8×Dic5, C22×D5×C22⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21128);