Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C22×#66266 |
| unambiguous semidirect product | D5⋊(C2×#520) |
| Fitting | C22×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ C22×#520 |
12270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,𝔽5)×H(5,𝔽2), #72258359, #72258376, … |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×H(5,𝔽2), #72258359, #72258376, … |
| maximal quotient of | #72242943 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116282);