Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D5×#1913 |
| Fitting | C5×#1913 ⋊ C2 |
| Sylow | C5 ⋊ C2×#1913 |
2078 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#12753, #72221752, #72242829, … |
| maximal normal subgroup of | D5×#12753, #72242829, AGL(1,𝔽5)×#1913, … |
| maximal quotient of | #72221752 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 171575);