Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C43 |
No aliases for this group.
| Fitting | C89×#1437 ⋊ C2 |
| Sylow | C89 ⋊ #13827 |
2878 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 427 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,b^2=h,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,i^d=i^882540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 91185);