Finite Group DatabasebetaFinite Group Databasebeta| order | 732 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C61 |
| unambiguous semidirect product | C3⋊(C4×C61) |
| derived, Sylow | C3 ⋊ C4×C61 |
| Hall | C3×C61 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C61 | D3 |
| commutator, hypocenter | C3 | C4×C61 |
| Frattini | C2 | D3×C61 |
| Fitting, socle, prime radical | C2×C3×C61 | C2 |
| cosocle | C2×C3 | C2×C61 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C61 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 732 |
366 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×D61, #13091764, #13091766, … |
| maximal normal subgroup of | Dic3×D61, #13091764, #13091766, … |
| maximal quotient of | C3⋊C8×C61, C2×Dic3×C61, Dic9×C61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(732, 3);