Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×#1277 ⋊ C2 |
| Sylow | C19 ⋊ #8930 |
426 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2432 |
Polycyclic presentation:
2^8,19|a^2=f,b^2=f,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^18,d^b=dg,e^b=eg,i^b=i^18,d^c=dg,e^c=eh,i^c=i^18556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 64047);