Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #7139 |
262 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bc,c^a=ch,i^a=i^88,d^b=dh3608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56402);