Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×C3⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | D3×C3⋊SL(2,ℤ/4) |
| unambiguous semidirect product | (C3×D3)⋊SL(2,ℤ/4) |
| unambiguous semidirect product | (D3×A4)⋊Dic3 |
| derived | C32×A4 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C3⋊S4 |
| commutator, hypocenter | C32×A4 | C2×C4 |
| Fitting, socle | C23×C32 | C2×D3 |
| prime radical | C2×C3×D3×A4 | C2 |
| cosocle | C2×C32×A4 | C22 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 ◁ C2 | |
371 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64204, D3×Dic3×S4, #13180296, … |
| maximal normal subgroup of | D3×#64204, D3×Dic3×S4, #13180296, … |
| maximal quotient of | D3×C3⋊(A4⋊C8), #13166006, #13166016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4170);