Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ #7452 |
102 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 49 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=fg,d^2=efgh,f^2=gh,g^2=h,b^a=bc,c^a=ce,i^a=i^18,c^b=cf,d^b=def,f^b=fg,g^b=gh,i^b=i^18445 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 57226);