Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #339×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1932 |
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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,b^2=df,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^88,e^c=eg,h^c=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1932×D89, C2×#26020922, #36557013, … |
| maximal normal subgroup of | #1932×D89, C2×#26020922, #36557013, … |
| maximal quotient of | #36452658, #36452665, #36452672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5180);