Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#14268636 |
| Fitting | C4×C8×C113 ⋊ C2 |
| Sylow | C113 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389373, C8×#14268636, #28389385, … |
| maximal normal subgroup of | #28389373, C8×#14268636, #28389385, … |
| maximal quotient of | C8×#14268636, #28389412, #28389419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 639);