Finite Group DatabasebetaFinite Group Databasebeta| order | 1764 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C3×D3×C72 |
| unambiguous semidirect product | C3⋊(C22×C3×C72) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C3×C72) |
| Fitting, socle | C2×C32×C72 ⋊ C2 |
| derived | C3 ⋊ C22×C3×C72 |
| Hall | C32×C72 ⋊ C22 |
| Sylow | C32 ⋊ C22×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C72 | D3 |
| commutator, cosocle, hypocenter | C3 | C22×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C72 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C72 | |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 588 |
882 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1764, 222);