Finite Group DatabasebetaFinite Group Databasebeta| order | 1764 |
| isoclinism | isoclinic class of D3×D7×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×D7×ΓL(1,𝔽8) |
| 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 | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 126 |
75 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1764, 163);