Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C89×#2102 ⋊ C2 |
| Sylow | C89 ⋊ #23751 |
664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=ef,c^2=e,e^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,e^b=eh,f^b=fh,d^c=dh,g^c=gh,i^d=i^881190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 199537);