Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D5×#3292 |
| Fitting | C5×#3292 ⋊ C2 |
| Sylow | C5 ⋊ C2×#3292 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D42×D5 |
| commutator, cosocle | C2×C4×C5 | C25 |
| Frattini | C2×C4 | C24×D5 |
| Fitting | C5×#3292 | C2 |
| socle | C2×C5 | C2×D42 |
| hypercenter | #3292 | D5 |
| hypocenter | C5 | C2×#3292 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #3292 | |
2766 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3292, D5×#61110, #72221472, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3292, D5×#61110, #72221472, … |
| maximal quotient of | #72223068, #72223454 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1045789);