Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×C22⋊Dic5 |
| Sylow | C5 ⋊ C23×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D5 |
| commutator | C2×C5 | C24×C4 |
| Frattini | C22 | C24×D5 |
| Fitting, prime radical | C26×C5 | C2 |
| socle | C25×C5 | C22 |
| cosocle | C22×C5 | C25 |
| hypercenter | C26 | D5 |
| hypocenter | C5 | C23×C22⋊C4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C25 ◁ C26 | |
4632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #11987222, #12004561, #12004597, … |
| maximal normal subgroup of | #11987222, #12004561, #12004597, … |
| maximal quotient of | C23×#3963, C22×C4×C22⋊Dic5, C22×#65536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21283);