Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | D42×C73 ⋊ C4 |
| Sylow | C73 ⋊ #34493 |
3076 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=h,c^2=g,d^2=gh,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^46,c^b=cg,d^b=df,i^d=i^27,i^h=i^72526 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1114604);