Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C82 · Schur multiplier (H2) = C42×C8 |
| direct product | C82×AGL(1,𝔽5) |
| Fitting | C5×C82 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C82 |
| Frattini | C42 | C22×AGL(1,𝔽5) |
| Fitting | C5×C82 | C4 |
| socle | C22×C5 | C43 |
| prime radical | C22×D5 | C2×C42 |
| cosocle | C42×D5 | C23 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C82 | |
750 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C82×#1043, AGL(1,𝔽5)×#1712, AGL(1,𝔽5)×#1705, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1712, AGL(1,𝔽5)×#1705, AGL(1,𝔽5)×#1455, … |
| maximal quotient of | C82×#1043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1085504);