Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C8×AGL(1,𝔽5) |
| Fitting | C22×C5×C8 ⋊ C4 |
| derived, Sylow | C5 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C22×C4×C8 |
| Frattini | C4 | C23×AGL(1,𝔽5) |
| Fitting | C22×C5×C8 | C4 |
| socle | C23×C5 | C42 |
| prime radical | C23×D5 | C2×C4 |
| cosocle | C4×D5 | C24 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C8 | |
760 conjugacy classes of subgroups; only the 418 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 418 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19476);