Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #1317 |
150 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 41 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=d,b^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^88,d^b=de,d^c=dg1258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36441776, #36441777, #36441798, … |
| maximal normal subgroup of | #36441776, #36441777, #36441798, … |
| maximal quotient of | #36441049, #36441057, #36441176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2440);