Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| isoclinism | isoclinic class of #90673 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×#90673 |
| unambiguous semidirect product | D113⋊(C23×C4) |
| Fitting, socle | C24×C113 ⋊ C4 |
| derived, Sylow | C113 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #90673 |
| commutator, hypocenter | C113 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C113 | C4 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C24 | |
1362 conjugacy classes of subgroups.
512 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1630);