Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | AΣL(1,𝔽16)×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2197 |
258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 258 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|b^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^88,e^b=efg,h^b=h^88,d^c=df,e^d=eg592 conjugacy classes — view the full character table.
| maximal subgroup of | #2197×D89, C2×#26022244, #36708446, … |
| maximal normal subgroup of | #2197×D89, C2×#26022244, #36708446, … |
| maximal quotient of | #36466464, #36466469, #36466503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6502);