Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #18033 |
598 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=fg,d^2=g,e^2=g,f^2=h,b^a=be,d^a=dg,e^a=eg,i^a=i^2,e^b=eg,i^b=i^4,d^c=dgh,i^c=i^2,i^d=i^4,i^f=i^477 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1102959);