Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#322×C89 ⋊ C2 |
| Sylow | C89 ⋊ #17320 |
826 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=f,e^2=g,f^2=h,b^a=bh,d^c=dg,i^d=i^883620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 135177);