Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of D3×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D3×D23 |
| unambiguous semidirect product | (D3×C23)⋊(C22×C3) |
| unambiguous semidirect product | (C3×D23)⋊(C22×C3) |
| unambiguous semidirect product | D69⋊(C22×C3) |
| Fitting, socle | C2×C32×C23 ⋊ C22 |
| derived | C3×C23 ⋊ C23×C3 |
| Hall | C32×C23 ⋊ C23 |
| Sylow | C23 ⋊ C22×C3×D3 |
| Sylow | C32 ⋊ C22×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D23 |
| commutator, cosocle, hypocenter | C3×C23 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C23 | C22 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C3 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 126);