Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#336 ⋊ C4 |
| Sylow | C5 ⋊ #7025 |
622 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=d,b^2=e,c^2=f,e^2=h,b^a=bc,c^a=cf,e^a=efg,i^a=i^2,c^b=cg,i^d=i^4116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1083500);