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×#1386 ⋊ C2 |
| Sylow | C89 ⋊ C4×#360 |
466 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=f,c^2=e,d^2=gh,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,d^b=dh,i^c=i^881472 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 84815);