Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C89×#2169 ⋊ C2 |
| Sylow | C89 ⋊ #33838 |
738 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|e^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,g^a=gh,i^a=i^88,c^b=ch,d^b=de,e^b=eg,g^b=gh,i^b=i^88,e^d=eg,g^d=gh,i^d=i^882507 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 326148);