Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | AΣL(1,𝔽16)×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2121 |
280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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=e,b^a=bd,d^a=df,f^a=fg,c^b=cg,e^b=ef,h^c=h^88,e^d=eg595 conjugacy classes — view the full character table.
| maximal subgroup of | #2121×D89, C2×#26021895, #36707168, … |
| maximal normal subgroup of | #2121×D89, C2×#26021895, #36707168, … |
| maximal quotient of | #36463515, #36463604, #36463685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6153);