Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | D5×#1781 |
| Fitting | C5×#1781 ⋊ C2 |
| Sylow | C5 ⋊ C2×#1781 |
6254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#23900, AGL(1,𝔽5)×#1781, #72242718, … |
| maximal normal subgroup of | D5×#23900, AGL(1,𝔽5)×#1781, #72242718, … |
| maximal quotient of | D5×#12687, D5×#8453, D5×#12707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 168688);