Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C162 · Schur multiplier (H2) = C16 |
| direct product | C16×#674 |
| derived, Sylow | C5 ⋊ C162 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C162 |
| Frattini | C4×C8 | C2×AGL(1,𝔽5) |
| Fitting | C4×C5×C16 | C4 |
| socle, prime radical | C22×C5 | C82 |
| cosocle | C8×#168 | C22 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C4×C16 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1083561);