Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#168 |
| derived, Sylow | C5 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D5 |
| commutator, hypocenter | C5 | C24×C8 |
| Frattini | C4 | C24×D5 |
| Fitting | C24×C4×C5 | C2 |
| socle, prime radical | C25×C5 | C4 |
| cosocle | C4×C5 | C25 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #12004523, #12004525, #12004549, … |
| maximal normal subgroup of | #12004523, #12004525, #12004549, … |
| maximal quotient of | C23×C4×#168, C23×C22⋊#168, C23×C4⋊#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21195);