Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4 |
| direct product | C22×#65780 |
| unambiguous semidirect product | D5⋊(C2×#390) |
| Fitting | C23×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C22×#390 |
9534 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,𝔽5)×#127, #72258341, #72258371, … |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×#127, #72258341, #72258371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114130);