Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #2216 |
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|a^2=g,b^2=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^b=h^881006 conjugacy classes — view the full character table.
| maximal subgroup of | #2216×D89, C2×#26022341, #36708864, … |
| maximal normal subgroup of | #2216×D89, C2×#26022341, #36708864, … |
| maximal quotient of | #36468637, #36468688, #36468756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6599);