Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D73⋊#1304 |
| Fitting | #379×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#1304 |
2414 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 172 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,b^a=bd,d^a=dg,f^a=fh,i^a=i^27,d^b=dh,e^b=eg,i^c=i^72,i^e=i^72556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1086786);