Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Sylow | C5 ⋊ #13824 |
2390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=h,c^2=eg,d^2=gh,b^a=be,c^a=cf,i^a=i^4,d^b=de,i^b=i^4,i^c=i^4212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 91172);