Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16813685 |
| unambiguous semidirect product | D113⋊#103 |
| Fitting | C2×Q8×C113 ⋊ C4 |
| Sylow | C113 ⋊ C2×#103 |
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
308 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16813685, #103×#90673, #28406346, … |
| maximal normal subgroup of | C4×#16813685, #103×#90673, #28406346, … |
| maximal quotient of | C2×Q8⋊#11744753, #28405863, C2×#20299448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1538);