Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×Dic5 |
| derived, Sylow | C5 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D5 |
| commutator, hypocenter | C5 | C25×C4 |
| Frattini | C2 | C25×D5 |
| Fitting, socle, prime radical | C26×C5 | C2 |
| cosocle | C2×C5 | C26 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C26 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10602337, Dic5×#379, #12030458, … |
| maximal normal subgroup of | C2×#10602337, Dic5×#379, #12030458, … |
| maximal quotient of | C24×C4×Dic5, C24×C22⋊Dic5, C24×C4⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21525);