Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C2×C42 |
| unambiguous semidirect product | C19⋊#7014 |
| Sylow | C19 ⋊ #7014 |
338 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4864 |
Polycyclic presentation:
2^8,19|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,b^a=bc,e^a=ef,d^b=df,i^b=i^18808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 56094);