Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C16 · Schur multiplier (H2) = C43 |
| direct product | C42×#674 |
| derived, Sylow | C5 ⋊ C42×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C42×C16 |
| Frattini | C22×C4 | C22×AGL(1,𝔽5) |
| Fitting | C43×C5 | C4 |
| socle, prime radical | C23×C5 | C22×C8 |
| cosocle | C22×#168 | C23 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C43 | |
558 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, 1095659);