Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×M16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2921 |
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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=f,c^2=e,f^2=g,b^a=be,d^a=dg,c^b=cg,h^b=h^881804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36451770, #36451772, #36451775, … |
| maximal normal subgroup of | #36451770, #36451772, #36451775, … |
| maximal quotient of | #36551907, #36551976, #36552336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 13146);