Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#3025 ⋊ C2 |
| Sylow | C5 ⋊ #33555 |
1146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,d^b=dh,f^b=fgh,i^b=i^4,e^c=eg,f^e=fh98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 323665);