Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C73 ⋊ #33485 |
548 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 238 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=f,c^2=f,d^2=e,f^2=g,g^2=h,b^a=be,c^a=ch,d^a=dh,i^a=i^46,c^b=ch,i^b=i^72,d^c=dh,i^c=i^27,i^d=i^72,i^f=i^72820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1113961);