Finite Group DatabasebetaFinite Group Databasebeta| order | 732 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C61 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C61 |
| unambiguous semidirect product | C3⋊(C22×C61) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C61) |
| Fitting, socle | C2×C3×C61 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C61 |
| Hall | C3×C61 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C61 | D3 |
| commutator, cosocle, hypocenter | C3 | C22×C61 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C61 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C61 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 366 |
366 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×Dic61, #13091765, #13091767, … |
| maximal normal subgroup of | D3×Dic61, #13091765, #13091767, … |
| maximal quotient of | Dic6×C61, C4×D3×C61, D12×C61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(732, 16);