Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×M16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1759 |
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 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=e,b^2=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^88,c^b=cg,h^b=h^881804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36446283, #36446285, #36446290, … |
| maximal normal subgroup of | #36446283, #36446285, #36446290, … |
| maximal quotient of | #36445033, #36445038, #36445053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4323);