Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#10598567 |
| Fitting | C2×C5×#99 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1390 |
1202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
74 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×AΣL(1,𝔽16), #72242710, #72242718, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×AΣL(1,𝔽16), #72242710, #72242718, … |
| maximal quotient of | #72242718 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1095808);