Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #7080 |
240 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 40 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=d,c^2=fh,d^2=g,e^2=h,f^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fh,i^a=i^27,c^b=cf,d^b=defh,e^b=eh,f^b=fh,d^c=dgh,i^d=i^72538 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1083620);