Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×#102×C89 ⋊ C2 |
| Sylow | C89 ⋊ #26723 |
874 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|c^2=eh,d^2=fh,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^88,c^b=cg,g^b=gh,g^c=gh2516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 237644);