Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D5×#3585 |
| Fitting | C5×#3585 ⋊ C2 |
| Sylow | C5 ⋊ C2×#3585 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D4×D5 |
| commutator, cosocle | C4×C5 | C26 |
| Frattini | C4 | C25×D5 |
| Fitting | C5×#3585 | C2 |
| socle | C2×C5 | C24×D4 |
| hypercenter | #3585 | D5 |
| hypocenter | C5 | C2×#3585 |
| LCS | G ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #3585 | |
11138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3585, D5×#23882, D5×#23872, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3585, D5×#23882, D5×#23872, … |
| maximal quotient of | #72221406, #72223301, D5×#60176 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1083403);