Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#410 ⋊ C4 |
| Sylow | C5 ⋊ #12573 |
838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=h,b^a=bd,d^a=dg,g^a=gh,e^b=eg,i^b=i^2,e^d=eh,i^f=i^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1095813);