Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×#1940 ⋊ C2 |
| Sylow | C19 ⋊ #8878 |
432 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^8,19|a^2=f,b^2=f,d^2=g,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,e^b=eh,i^b=i^18,d^c=dh,e^c=eg,i^c=i^18442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 63699);