Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C73 ⋊ #12586 |
746 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 144 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=f,d^2=h,e^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,i^a=i^27,c^b=ch,e^b=egh,i^c=i^72,e^d=eh,i^e=i^72550 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1095874);