Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | #64408⋊#349 |
| Sylow | C73 ⋊ C4×#349 |
522 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 141 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=e,b^2=f,c^2=e,f^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^46,d^b=dh,i^b=i^10,i^c=i^46,i^e=i^72,i^f=i^27,i^g=i^72268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1117675);