Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #2220 |
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^b=h^88994 conjugacy classes — view the full character table.
| maximal subgroup of | #2220×D89, C2×#26022363, #36708890, … |
| maximal normal subgroup of | #2220×D89, C2×#26022363, #36708890, … |
| maximal quotient of | #36468659, #36468710, #36468778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6621);