Finite Group DatabasebetaFinite Group Databasebeta| order | 3732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D311 |
| unambiguous semidirect product | (D3×C311)⋊C2 |
| unambiguous semidirect product | (C3×D311)⋊C2 |
| unambiguous semidirect product | D933⋊C2 |
| Fitting, socle, derived, Hall | C3×C311 ⋊ C22 |
| Sylow | C311 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C311 | C22 |
| LCS | G ▷ C3×C311 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 314 |
| transitive degree | μt(G) = 933 |
471 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D311, C3×D3×D311, C3⋊D3×D311, … |
| maximal normal subgroup of | C3×D3×D311, D3×D311⋊C5, C5×D3×D311, … |
| maximal quotient of | D9×D311, C3×D3×D311, C3⋊D3×D311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3732, 6);