Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of A4×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×D23 |
| unambiguous semidirect product | C23⋊(C2×C3×A4) |
| unambiguous semidirect product | (C22×D23)⋊C32 |
| unambiguous semidirect product | (C22×C3×D23)⋊C3 |
| Fitting, socle | C22×C3×C23 ⋊ C2×C3 |
| derived | C22×C23 ⋊ C2×C32 |
| Hall | C22×D23 ⋊ C32 |
| Sylow | C23 ⋊ C2×C3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×D23 |
| commutator, cosocle, hypocenter | C22×C23 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C23 | C2×C3 |
| LCS | G ▷ C22×C23 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 121);