Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C22×D5×C16 |
| Fitting | C22×C5×C16 ⋊ C2 |
| derived, Sylow | C5 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D5 |
| commutator, hypocenter | C5 | C23×C16 |
| Frattini | C8 | C23×D5 |
| Fitting | C22×C5×C16 | C2 |
| socle | C23×C5 | C2×C8 |
| prime radical | C23×D5 | C8 |
| cosocle | C5×C8 | C24 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C16 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1374, #12014141, D5×#1379, … |
| maximal normal subgroup of | D5×#1374, #12014141, D5×#1379, … |
| maximal quotient of | C2×C4×D5×C16, C22×C16×Dic5, C2×D5×C22⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15811);