Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C89×#1944 ⋊ C2 |
| Sylow | C89 ⋊ #26399 |
814 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=fh,b^2=fh,c^2=fh,d^2=h,e^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^88,c^b=cg,d^b=dh,e^b=eh,i^b=i^88,i^c=i^88,e^d=eh,i^d=i^881454 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 232991);