Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #486×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3184 |
446 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^88,d^c=dg,h^c=h^88,h^d=h^881000 conjugacy classes — view the full character table.
| maximal subgroup of | #36530753, #36530755, #36530757, … |
| maximal normal subgroup of | #36530753, #36530755, #36530757, … |
| maximal quotient of | #36555025, #36558740, #36559676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 15247);