Finite Group DatabasebetaFinite Group Databasebeta| order | 1764 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽8)⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×ΓL(1,𝔽8)⋊D7 |
| unambiguous semidirect product | (D3×ΓL(1,𝔽8))⋊D7 |
| Fitting, socle, derived | C3×C72 ⋊ C22×C3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C72 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72 | C22×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1764, 162);