Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #1571 |
168 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 89 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=df,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^88,c^b=cg,h^b=h^881270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36448448, #36448449, #36448459, … |
| maximal normal subgroup of | #36448448, #36448449, #36448459, … |
| maximal quotient of | #36443905, #36445643, #36447278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3286);