Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | #322×C73 ⋊ C4 |
| Sylow | C73 ⋊ #7843 |
526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,b^a=bh,c^b=cg,i^c=i^27,i^f=i^72832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1085523);