Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #13495 |
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=e,c^2=d,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,c^b=cf,f^b=fh,e^c=eg,f^c=fh,g^c=gh,i^c=i^722056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 89441);