Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#16813534 |
| Fitting | C22×C8×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388497, #28390331, C4×#16813534, … |
| maximal normal subgroup of | #28388497, #28390331, C4×#16813534, … |
| maximal quotient of | C2×#20298321, C2×#20298323, #28388886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 509);