Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #8155 |
710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=f,c^2=eg,f^2=h,b^a=bd,c^a=ch,f^a=fg,i^a=i^88,d^b=dg3584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 60092);