Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #13109 |
306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22784 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=f,c^2=d,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^b=i^88,e^c=eg,g^c=gh1994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 87216);