Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C89×#2108 ⋊ C2 |
| Sylow | C89 ⋊ C4×#504 |
834 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=f,e^2=g,g^2=h,i^b=i^88,d^c=dh,i^d=i^883680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 322212);