Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C4×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ #34197 |
2314 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=f,c^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,i^a=i^2,d^b=df,i^h=i^4128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114308);