Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C89 ⋊ #1851 |
324 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 109 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,b^2=f,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^b=h^881804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36441073, #36441075, #36448532, … |
| maximal normal subgroup of | #36441073, #36441075, #36448532, … |
| maximal quotient of | #36448272, #36448277, #36448282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4692);