Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#509×C73 ⋊ C2 |
| Sylow | C73 ⋊ #33539 |
1130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fh,g^a=gh,e^b=eg,g^b=gh,i^b=i^72,f^c=fh,i^c=i^721192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 323533);