Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#16813696 |
| Sylow | C113 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#90673 |
| commutator | C2×C113 | C22×C8 |
| Frattini | C4 | C22×#90673 |
| Fitting | C22×C4×C113 | C4 |
| socle | C22×C113 | C2×C8 |
| hypercenter | C22×C4 | #90673 |
| hypocenter | C113 | C2×M32 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
90 conjugacy classes of subgroups.
488 conjugacy classes — view the full character table.
| maximal subgroup of | #28405615, #28405616, #28405618, … |
| maximal normal subgroup of | #28405615, #28405616, #28405618, … |
| maximal quotient of | C2×#20299486, C4×#16813696, C2×C22⋊#14268650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1604);