Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C82×C73 ⋊ C2 |
| Sylow | C73 ⋊ #17328 |
750 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,e^2=g,f^2=h,c^a=ch,d^c=dg,i^c=i^724720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 135229);