Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C22×C5×#120 ⋊ C2 |
| Sylow | C5 ⋊ #23900 |
3520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|b^a=be,c^a=cf,d^a=de,c^b=cg,f^b=fh,e^c=eh,i^c=i^4,f^d=fh158 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#23900, #72242893, #72242908, … |
| maximal normal subgroup of | D5×#23900, #72242893, #72242908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 201145);