Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ #12767 |
878 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^72,e^b=egh,f^b=fg,d^c=dg,f^c=fh,e^d=eh,f^d=fh1402 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 85413);