Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C19×#431 ⋊ C2 |
| Sylow | C19 ⋊ #9134 |
728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2432 |
Polycyclic presentation:
2^8,19|a^2=f,b^2=dfgh,c^2=h,d^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^18,d^b=dh,f^b=fh778 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 65238);