Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×Q8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #8171 |
598 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=eg,d^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fg,c^b=cg,i^b=i^10,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, 1116856);