Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C89×#1604 ⋊ C2 |
| Sylow | C89 ⋊ #18231 |
1200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=i^88,e^b=eg,f^b=fh,i^b=i^88,d^c=dg,e^c=eh,i^d=i^881049 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 142809);