Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #1763 |
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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^2=f,c^2=eg,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^88,c^b=cg,h^c=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1763×D89, C2×#26020084, #36552197, … |
| maximal normal subgroup of | #1763×D89, C2×#26020084, #36552197, … |
| maximal quotient of | #36445037, #36445047, #36445072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4342);