Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C2 |
| direct product | D3×A4×C23 |
| unambiguous semidirect product | C3⋊(C2×A4×C23) |
| unambiguous semidirect product | (C22×D3)⋊(C3×C23) |
| unambiguous semidirect product | (C22×D3×C23)⋊C3 |
| Fitting, socle | C22×C3×C23 ⋊ C2×C3 |
| derived | C22×C3 ⋊ C2×C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×A4 |
| commutator, cosocle, hypocenter | C22×C3 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C23 | C2×C3 |
| LCS | G ▷ C22×C3 | |
| UCS | C1 ◁ C23 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 276 |
276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 122);