Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ #17430 |
884 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 230 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,b^2=g,c^2=gh,d^2=gh,f^2=h,b^a=be,e^a=eg,i^a=i^27,f^b=fg,i^b=i^72,d^c=dgh,i^f=i^72775 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1099926);