Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #20528 |
1250 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 344 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=f,b^2=g,f^2=h,b^a=be,d^a=de,i^a=i^27,c^b=ceh,d^b=dh,i^f=i^72604 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1104153);