Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #365×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2180 |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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,c^2=ef,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,d^b=dfg,e^b=eg,f^b=fg,h^b=h^88,d^c=dg,h^c=h^88727 conjugacy classes — view the full character table.
| maximal subgroup of | #2180×D89, C2×#26022142, #36707875, … |
| maximal normal subgroup of | #2180×D89, C2×#26022142, #36707875, … |
| maximal quotient of | #36466300, #36466307, #36466378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6400);