Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #1937 |
230 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 81 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,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^88,h^b=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1937×D89, C2×#26020958, #36557174, … |
| maximal normal subgroup of | #1937×D89, C2×#26020958, #36557174, … |
| maximal quotient of | #36452687, #36452694, #36452729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5216);