Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #9973 |
632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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=g,b^2=gh,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,i^a=i^18,c^b=cf,d^b=dg,f^b=fg,i^b=i^18,d^c=dh,f^c=fg,i^c=i^18436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 70164);