Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C4 |
| direct product | D3×C42⋊C9 |
| unambiguous semidirect product | C3⋊(C2×C42⋊C9) |
| unambiguous semidirect product | (C42×D3)⋊C9 |
| derived | C3×C42 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C42⋊C3 |
| commutator, hypocenter | C3×C42 | C2×C9 |
| Frattini | C22×C3 | D3×A4 |
| Fitting, cosocle | C32×C42 | C2×C3 |
| socle | C22×C32 | C2×A4 |
| prime radical | C22×C3×D3 | A4 |
| LCS | G ▷ C3×C42 | |
| UCS | C1 ◁ C3 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63419, C2×D3×C42⋊C9, D3×#126⋊C9, … |
| maximal normal subgroup of | D3×#63419, C2×D3×C42⋊C9, D3×#126⋊C9, … |
| maximal quotient of | C3⋊(#376⋊C9), D3×#95⋊C9, Dic3×C42⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 723);