Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #66297 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#66297 |
| unambiguous semidirect product | ((C24⋊C5)⋊C2)⋊C4 |
| Fitting, socle | C25 ⋊ AGL(1,𝔽5) |
| derived | C24⋊C5 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #66297 |
| commutator, hypocenter | C24⋊C5 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25 | AGL(1,𝔽5) |
| prime radical | C2×(C24⋊C5)⋊C2 | C2 |
| cosocle | (C24⋊C5)⋊C2 | C22 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C2 | |
161 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10 |
22 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21536);