Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×#1803 ⋊ C2 |
| Sylow | C5 ⋊ #21898 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=h,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^4,c^b=ce,d^b=dh,i^b=i^4,f^c=fh128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 179567);