Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #7375 |
228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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=e,d^2=f,e^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,c^b=cg,d^b=deh,g^b=gh,i^b=i^72,d^c=dgh,e^c=eh,e^d=eh970 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 56993);