Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C89×#1527 ⋊ C2 |
| Sylow | C89 ⋊ #17685 |
1152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=f,e^2=h,f^2=g,b^a=be,e^a=eg,e^b=eh,f^b=fgh,i^b=i^88,d^c=dh,i^c=i^88,i^d=i^881460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 137784);