Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #99×C73 ⋊ C8 |
| Sylow | C73 ⋊ #7204 |
380 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^8,73|a^2=d,b^2=e,d^2=g,e^2=gh,b^a=bc,c^a=cf,f^a=fh,i^a=i^22,d^b=df,i^b=i^10,d^c=dh,i^d=i^46,i^e=i^27,i^g=i^72151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116560);