Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D5×#3484 |
| Fitting | C5×#3484 ⋊ C2 |
| Sylow | C5 ⋊ C2×#3484 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D5 |
| commutator, socle, cosocle | C22×C5 | C26 |
| Fitting | C5×#3484 | C2 |
| hypercenter | #3484 | D5 |
| hypocenter | C5 | C2×#3484 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #3484 | |
14438 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3484, D5×#23882, #72221450, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3484, D5×#23882, #72221450, … |
| maximal quotient of | C5⋊D5×#3484, D5×#35346 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1077443);