Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C89×#2322 ⋊ C2 |
| Sylow | C89 ⋊ C4×#536 |
2962 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=h,b^2=f,c^2=f,e^2=h,b^a=bf,c^a=cg,d^a=df,c^b=cf,i^b=i^88,i^e=i^882024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 328608);