Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#11744753 |
| Sylow | C113 ⋊ C2×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#90673 |
| commutator | C2×C113 | C22×C8 |
| Frattini | C22 | C22×#90673 |
| Fitting | C24×C113 | C4 |
| socle | C23×C113 | C2×C4 |
| hypercenter | C24 | #90673 |
| hypocenter | C113 | C2×C22⋊C8 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C24 | |
202 conjugacy classes of subgroups.
488 conjugacy classes — view the full character table.
| maximal subgroup of | #28405412, #28405417, C2×#20299441, … |
| maximal normal subgroup of | #28405412, #28405417, C2×#20299441, … |
| maximal quotient of | C2×#20299441, C2×#20299443, #28405805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1516);