Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #529×C73 ⋊ C4 |
| Sylow | C73 ⋊ #34350 |
2106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=h,d^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dfg,i^a=i^27,c^b=cfg,d^b=df,i^h=i^72580 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1114461);