Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C89×#1780 ⋊ C2 |
| Sylow | C89 ⋊ #20580 |
3958 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 3958 conjugacy classes of subgroups — too many to draw. Only its 387 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|a^2=g,g^2=h,b^a=be,c^a=cf,d^a=dh,c^b=ch,i^d=i^882000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 168679);