Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×H(3,ℤ/4)×C73 ⋊ C2 |
| Sylow | C73 ⋊ #10743 |
1208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^72,e^b=eh,d^c=dh,i^c=i^721642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 74902);