Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#90673 |
| unambiguous semidirect product | D113⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#90673)⋊C23 |
| Fitting | C24×C113 ⋊ C4 |
| Sylow | C113 ⋊ C22×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#90673 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C2 | C23×#90673 |
| Fitting | C24×C113 | C4 |
| socle | C23×C113 | C2×C4 |
| hypercenter | C24 | #90673 |
| hypocenter | C113 | C22×C22⋊C4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C24 | |
674 conjugacy classes of subgroups.
488 conjugacy classes — view the full character table.
| maximal subgroup of | #28405747, #28405748, #28405755, … |
| maximal normal subgroup of | #28405747, #28405748, #28405755, … |
| maximal quotient of | C22×(C2×#90673)⋊C4, C2×C4×C22⋊#90673, C2×#20299539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1610);