Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C22×#66258 |
| unambiguous semidirect product | D5⋊(C2×#518) |
| Fitting | C23×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C22×#518 |
14590 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), #72242760, #72242763, … |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×H(5,𝔽2), #72242760, #72242763, … |
| maximal quotient of | #72242923, #72242948 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116280);