Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C2 |
| direct product | A4×C3⋊C32 |
| unambiguous semidirect product | C3⋊(A4×C32) |
| unambiguous semidirect product | (C22×C3⋊C32)⋊C3 |
| derived | C22×C3 ⋊ C3×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D3×A4 |
| commutator, hypocenter | C22×C3 | C3×C32 |
| Fitting, cosocle | C22×C3×C16 | C2×C3 |
| socle | C23×C3 | C3×C16 |
| prime radical | C2×C3×A4 | C16 |
| LCS | G ▷ C22×C3 | |
| UCS | C1 ◁ C16 | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 288 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154176);