Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #7919 |
626 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 168 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=e,b^2=f,e^2=h,f^2=g,b^a=bd,c^a=ch,d^a=dg,i^a=i^27,e^b=eg,i^c=i^72,i^e=i^72784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1085840);