Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of C3⋊D3×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3⋊D3×D23 |
| Fitting, socle | C2×C32×C23 ⋊ C22 |
| derived, 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 | C32×C23 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C23 | C22 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 414 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 127);