Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C73 ⋊ #7053 |
122 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18688 |
Polycyclic presentation:
2^8,73|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,f^2=h,b^a=be,d^a=dg,i^a=i^27,c^b=cg,i^c=i^721240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1083566);