Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of #66297 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#66297 |
| Fitting | C24×C4 ⋊ AGL(1,𝔽5) |
| derived | C24⋊C5 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #66297 |
| commutator, hypocenter | C24⋊C5 | C42 |
| Frattini | C2 | C2×#66297 |
| Fitting | C24×C4 | AGL(1,𝔽5) |
| socle | C25 | C2×AGL(1,𝔽5) |
| prime radical, cosocle | C2×(C24⋊C5)⋊C2 | C22 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C4 | |
317 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 317 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11757163⋊C2, C4×AΣL(2,𝔽4), C4×AΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116370);