Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #342×C73 ⋊ C4 |
| Sylow | C73 ⋊ #11287 |
1118 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 1118 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) = 1168 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=e,c^2=d,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^27,c^b=cf,d^b=dh,f^b=fh,g^b=gh,e^c=eh,f^c=fh,g^c=gh,i^g=i^72448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1093086);