Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | #64408⋊(C22⋊C16) |
| Sylow | C73 ⋊ C4×C22⋊C16 |
614 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=e,f^2=g,g^2=h,b^a=bd,i^a=i^46,i^b=i^10,i^c=i^46,i^e=i^72,i^f=i^27,i^g=i^72448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1117666);