Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C19×#2011 ⋊ C2 |
| Sylow | C19 ⋊ #7742 |
668 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2432 |
Polycyclic presentation:
2^8,19|b^2=f,c^2=fg,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,d^b=df,e^b=eg,i^b=i^18,d^c=dg,e^c=eh325 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 58312);