Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C89×#1283 ⋊ C2 |
| Sylow | C89 ⋊ #8166 |
494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=f,c^2=e,e^2=h,f^2=g,b^a=bd,c^a=ch,f^a=fg,d^b=dg,i^b=i^88,i^c=i^882000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 60147);