Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #362×C73 ⋊ C4 |
| Sylow | C73 ⋊ #12648 |
422 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 102 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=e,b^2=f,c^2=eh,d^2=g,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,i^a=i^46,c^b=cg,e^b=eh,i^b=i^46,d^c=dh,f^c=fh,i^c=i^27,i^e=i^72,i^f=i^72334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1096185);