Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C4×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ #13817 |
1970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=h,c^2=g,d^2=fg,b^a=be,c^a=cf,d^b=de,i^b=i^2,i^h=i^4140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098298);