Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | D4⋊C8×C73 ⋊ C4 |
| Sylow | C73 ⋊ #8890 |
602 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=fh,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^46,d^b=dg,e^b=eh,i^b=i^27,d^c=dh,e^c=eh,i^f=i^72556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1089248);