Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C22×H(5,𝔽2)×C89 ⋊ C2 |
| Sylow | C89 ⋊ #32884 |
3994 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3994 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^88,e^b=eh,d^c=dh3044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 318238);