Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C24 |
| direct product | D3×C22⋊(C22⋊C9) |
| unambiguous semidirect product | C3⋊(C2×C22⋊(C22⋊C9)) |
| derived | C24×C3 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D3×C22⋊A4 |
| commutator, hypocenter | C24×C3 | C2×C9 |
| Fitting, socle, cosocle | C24×C32 | C2×C3 |
| prime radical | C24×C3×D3 | C3 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C3 | |
598 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#120⋊C9, D3×#64188, C2×D3×C22⋊(C22⋊C9) |
| maximal normal subgroup of | D3×#120⋊C9, D3×#64188, C2×D3×C22⋊(C22⋊C9) |
| maximal quotient of | C3⋊#10593123, D3×C22⋊(Q8⋊C9), C3⋊#10593125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4029);