Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #1973 |
340 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 113 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=eg,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^88,c^b=cg,h^b=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1973×D89, C2×#26021135, #36558276, … |
| maximal normal subgroup of | #1973×D89, C2×#26021135, #36558276, … |
| maximal quotient of | #36453308, #36453342, #36453606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5393);