Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C19×H(3,ℤ/4) ⋊ C2 |
| Sylow | C19 ⋊ #10949 |
990 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^8,19|a^2=f,b^2=g,c^2=ef,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,e^b=eh,f^b=fh,i^b=i^18,d^c=dh,i^c=i^18454 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 75965);