Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C5×#1889 ⋊ C2 |
| Sylow | C5 ⋊ C4×B(4,𝔽2) |
1910 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=g,b^a=be,c^a=cf,i^a=i^4,f^b=fh,e^c=eh,i^c=i^4,i^d=i^4128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 175553);