Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#2062 ⋊ C2 |
| Sylow | C5 ⋊ #25852 |
1262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,c^b=cg,f^b=fh,g^c=gh,i^d=i^495 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 225710);