Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×#1374 ⋊ C2 |
| Sylow | C19 ⋊ #7102 |
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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|a^2=d,c^2=f,d^2=g,g^2=h,b^a=bc,c^a=ce,c^b=cf,d^b=def,i^b=i^18796 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 56311);