Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #486×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1677 |
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 53 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=dg,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 | #1677×D89, C2×#26019658, #36536733, … |
| maximal normal subgroup of | #1677×D89, C2×#26019658, #36536733, … |
| maximal quotient of | #36447489, #36450570, #36450612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3916);