Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q32×C73 ⋊ C8 |
| Sylow | C73 ⋊ #7386 |
124 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 35 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|a^2=d,b^2=h,c^2=egh,d^2=f,e^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^10,c^b=ceh,d^b=dh,e^b=eg,g^b=gh,i^d=i^27,i^f=i^72151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116674);