Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×#90673)⋊C4 |
| unambiguous semidirect product | D113⋊#95 |
| Fitting | C22×C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ C2×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#90673 |
| commutator | C2×C113 | C2×C42 |
| Frattini | C22 | C22×#90673 |
| Fitting | C22×C4×C113 | C4 |
| socle | C23×C113 | C2×C4 |
| hypercenter | C22×C4 | #90673 |
| hypocenter | C113 | C2×#95 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 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 | #28405411, #28405447, #28405449, … |
| maximal normal subgroup of | #28405411, #28405447, #28405449, … |
| maximal quotient of | C4×(C2×#90673)⋊C4, #28405747, #28405748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1484);