Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16813701 |
| unambiguous semidirect product | D113⋊#117 |
| Fitting | C22×C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
488 conjugacy classes — view the full character table.
| maximal subgroup of | #28406239, #28406242, C2×#20299465, … |
| maximal normal subgroup of | #28406239, #28406242, C2×#20299465, … |
| maximal quotient of | C2×#20299534, C2×C4×C22⋊#90673, C2×C4×C4⋊#90673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1612);