Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C89×#1757 ⋊ C2 |
| Sylow | C89 ⋊ #12623 |
470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=f,c^2=e,e^2=h,b^a=bd,f^a=fg,i^a=i^88,d^b=dg,g^b=gh,f^d=fh1988 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 84722);