Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | AGL(1,𝔽5)×#564 |
| Fitting | C5×#564 ⋊ C4 |
| Sylow | C5 ⋊ C4×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×AGL(1,𝔽5) |
| commutator, socle | C22×C5 | C24×C4 |
| Fitting | C5×#564 | C4 |
| prime radical, cosocle | C22×D5 | C25 |
| hypercenter | #564 | AGL(1,𝔽5) |
| hypocenter | C5 | C4×#564 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #564 | |
1800 conjugacy classes of subgroups; only the 776 normal subgroups are shown.
This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 776 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114466);