Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #11869 |
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 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) = 4672 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=h,c^2=gh,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=cg,d^a=df,g^a=gh,i^a=i^72,c^b=cf,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^b=i^72,d^c=dh,e^d=eh1618 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 80567);