Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #497×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1659 |
228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,d^c=dg,e^c=efg,h^c=h^88724 conjugacy classes — view the full character table.
| maximal subgroup of | #36475167, #36475170, #1659×D89, … |
| maximal normal subgroup of | #36475167, #36475170, #1659×D89, … |
| maximal quotient of | #36443213, #36443242, #36443259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3814);