Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #7572 |
884 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=e,d^2=g,e^2=h,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,i^b=i^883584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 57552);