Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C89×#1466 ⋊ C2 |
| Sylow | C89 ⋊ #17415 |
1008 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=f,c^2=gh,d^2=h,f^2=h,b^a=be,e^a=eg,i^a=i^88,f^b=fg,d^c=dh,i^d=i^881463 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 135786);