Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #423×C73 ⋊ C4 |
| Sylow | C73 ⋊ #20431 |
1146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=ef,g^2=h,b^a=be,d^a=dh,i^a=i^46,i^b=i^46,d^c=dh,i^c=i^27,i^f=i^72,i^g=i^72604 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1103764);