Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C73 ⋊ #60344 |
1664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=f,c^2=f,e^2=g,g^2=h,b^a=bf,c^a=ch,d^a=df,i^a=i^46,c^b=cf,d^b=dh,e^b=eh,i^c=i^72,i^e=i^27,i^g=i^72472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116239);