Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊#90673 |
| Fitting | C22×C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #28405415, #28405416, #28405421, … |
| maximal normal subgroup of | #28405415, #28405416, #28405421, … |
| maximal quotient of | C4×(C2×#90673)⋊C4, #28405748, #28405750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1486);