Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | #64408⋊#324 |
| Fitting | C2×C4⋊C4×C73 ⋊ C8 |
| Sylow | C73 ⋊ C4×#324 |
730 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=eg,f^2=h,b^a=bd,f^a=fg,i^a=i^46,d^b=dg,i^b=i^10,i^c=i^46,i^e=i^72,i^f=i^27,i^h=i^72268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116847);