Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #500×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1675 |
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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=fg,b^2=df,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,e^c=eg,h^c=h^88997 conjugacy classes — view the full character table.
| maximal subgroup of | #36468233, #36468235, #36468240, … |
| maximal normal subgroup of | #36468233, #36468235, #36468240, … |
| maximal quotient of | #36447479, #36450570, #36452780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3906);