Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | D3×C9⋊C16 |
| unambiguous semidirect product | (D3×C9)⋊C16 |
| derived, Sylow | C3×C9 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D3×D9 |
| commutator, hypocenter | C3×C9 | C2×C16 |
| Frattini | C3×C8 | D32 |
| Fitting, cosocle | C3×C8×C9 | C22 |
| socle | C2×C32 | C2×C3⋊C8 |
| prime radical | C2×C3×D3 | C3⋊C8 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C8 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C16×D9, D3×#63357, #13136963, … |
| maximal normal subgroup of | D3×C16×D9, D3×#63357, #13136963, … |
| maximal quotient of | D3×C9⋊C32, #13134900, Dic3×C9⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 203);