Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C43 |
No aliases for this group.
| Fitting | C2×#97×C73 ⋊ C4 |
| Sylow | C73 ⋊ C4×H(3,ℤ/4) |
954 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 264 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,c^2=g,d^2=h,b^a=bd,f^a=fh,i^a=i^46,e^b=eh,i^b=i^27,i^c=i^72,i^e=i^72,i^f=i^72808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1091842);