Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #8246 |
376 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=eh,d^2=g,e^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fgh,i^a=i^46,c^b=ch,d^b=dh,i^c=i^27,i^e=i^72406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1087428);