Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C89×M128 ⋊ C2 |
| Sylow | C89 ⋊ #7513 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,c^a=ch,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, 57378);