Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#10603804 |
| unambiguous semidirect product | D5⋊#1444 |
| Fitting | C2×C5×#95 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1444 |
3550 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #72221500, C2×AGL(1,𝔽5)×#392, #72258371 |
| maximal normal subgroup of | #72221500, C2×AGL(1,𝔽5)×#392, #72258371 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098338);