Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D5×#3025 |
| Fitting | C5×#3025 ⋊ C2 |
| Sylow | C5 ⋊ C2×#3025 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D5×#120 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C5×#3025 | C2 |
| socle | C2×C5 | C22×#120 |
| hypercenter | #3025 | D5 |
| hypocenter | C5 | C2×#3025 |
| LCS | G ▷ C23×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #3025 | |
5086 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#23882, #72221452, AGL(1,𝔽5)×#3025, … |
| maximal normal subgroup of | D5×#23882, #72221452, AGL(1,𝔽5)×#3025, … |
| maximal quotient of | #72226507 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1036287);