Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#14268657 |
| Sylow | C113 ⋊ C22×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#90673 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C2 | C23×#90673 |
| Fitting | C22×C4×C113 | C4 |
| socle | C23×C113 | C2×C4 |
| hypercenter | C22×C4 | #90673 |
| hypocenter | C113 | C22×M16 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
298 conjugacy classes of subgroups.
488 conjugacy classes — view the full character table.
| maximal subgroup of | #28406238, #28406241, C2×#20299468, … |
| maximal normal subgroup of | #28406238, #28406241, C2×#20299468, … |
| maximal quotient of | C22×#16813677, C2×C4×#14268657, C22×#16813679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1623);