Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C89×#1790 ⋊ C2 |
| Sylow | C89 ⋊ #32898 |
4360 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|b^a=be,c^a=cf,d^a=dg,i^a=i^88,f^b=fh,e^c=eh,i^d=i^881457 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 318340);