Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C73×#3027 ⋊ C2 |
| Sylow | C73 ⋊ #13353 |
720 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fgh,i^a=i^72,c^b=cf,d^b=dh,g^b=gh,d^c=dg,e^c=eh,f^d=fh1072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 88570);