Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #23382 |
606 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=g,c^2=e,d^2=f,g^2=h,b^a=be,c^a=cf,d^a=def,i^a=i^27,c^b=cefh,d^b=deh,i^b=i^72,d^c=dh,i^g=i^72448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1113353);