Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C89×#1742 ⋊ C2 |
| Sylow | C89 ⋊ #10939 |
1058 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=g,c^2=ef,g^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^88,d^b=dh,e^b=eh,f^b=fh,i^b=i^88,d^c=dh1994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 75905);