Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16813680 |
| Fitting | C24×C113 ⋊ C4 |
| Sylow | C113 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
470 conjugacy classes — view the full character table.
| maximal subgroup of | #28405658, #28405659, C4×#16813680, … |
| maximal normal subgroup of | #28405658, #28405659, C4×#16813680, … |
| maximal quotient of | C2×#20299441, C2×#20299444, #28405809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1525);