Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C19×#398 ⋊ C2 |
| Sylow | C19 ⋊ #9919 |
716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^8,19|b^2=h,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,i^a=i^18,c^b=cf,d^b=dg,d^c=dh436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 69799);