Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#399×C89 ⋊ C2 |
| Sylow | C89 ⋊ #9920 |
856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|b^2=gh,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,i^a=i^88,c^b=cf,d^b=dg,d^c=dh1976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 69806);