Finite Group DatabasebetaFinite Group Databasebeta| order | 2034 |
| isoclinism | isoclinic class of D339 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D339 |
| unambiguous semidirect product | C3⋊(C3×D113) |
| unambiguous semidirect product | C113⋊(C3×D3) |
| Fitting, socle, Hall | C32×C113 ⋊ C2 |
| derived | C3×C113 ⋊ C2×C3 |
| Sylow | C113 ⋊ C3×D3 |
| Sylow | C32 ⋊ D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D339 |
| commutator, cosocle, hypocenter | C3×C113 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C113 | C2 |
| LCS | G ▷ C3×C113 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 678 |
513 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D113, D3×D339, (C3⋊D3)⋊D113, … |
| maximal normal subgroup of | C3×D3×D113, D3×D339, (C3⋊D3)⋊D113, … |
| maximal quotient of | C3×Dic339, C2×C3×D339, C3⋊(ΓL(1,𝔽8)⋊D113), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2034, 8);