Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11744753 |
| derived, Sylow | C113 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #90673 |
| commutator, hypocenter | C113 | C2×C4×C8 |
| Frattini | C22 | C22×#90673 |
| Fitting | C22×C4×C113 | C4 |
| socle | C23×C113 | C2×C4 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C22×C4 | |
162 conjugacy classes of subgroups.
512 conjugacy classes — view the full character table.
| maximal subgroup of | #28405396, #28405407, #28405410, … |
| maximal normal subgroup of | #28405396, #28405407, #28405410, … |
| maximal quotient of | C2×C8×#11744753, C2×#20299439, M16×#11744753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1504);