Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×#405×C89 ⋊ C2 |
| Sylow | C89 ⋊ #20420 |
1474 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=g,c^2=f,e^2=h,f^2=h,b^a=be,e^a=eh,g^a=gh,i^a=i^88,d^b=dh,i^b=i^883608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 167417);