Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11744762 |
| unambiguous semidirect product | #90673⋊(C2×C8) |
| Fitting | C2×C4×C113 ⋊ C8 |
| derived, Sylow | C113 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11744762 |
| commutator, hypocenter | C113 | C2×C4×C8 |
| Frattini | C2 | C22×#11744762 |
| Fitting | C2×C4×C113 | C8 |
| socle | C22×C113 | C2×C8 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C4 | |
162 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11744762)⋊C8, #28407581, #28407582, … |
| maximal normal subgroup of | (C2×#11744762)⋊C8, #28407581, #28407582, … |
| maximal quotient of | C2×C8×#11744762, C2×#20299682, M16×#11744762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1659);