Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #21075 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=g,b^2=eg,c^2=e,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^88,i^b=i^88,f^c=fh2000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 172118);