Finite Group DatabasebetaFinite Group Databasebeta| order | 2068 |
| isoclinism | isoclinic class of D11×D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D47 |
| unambiguous semidirect product | (D11×C47)⋊C2 |
| unambiguous semidirect product | (C11×D47)⋊C2 |
| unambiguous semidirect product | D517⋊C2 |
| Fitting, socle, derived, Hall | C11×C47 ⋊ C22 |
| Sylow | C47 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C47 | C22 |
| LCS | G ▷ C11×C47 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 517 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D11×D47, D47×D77, D11×D329, … |
| maximal normal subgroup of | C7×D11×D47, C11×D11×D47, C13×D11×D47, … |
| maximal quotient of | C7×D11×D47, D47×D77, D11×D329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2068, 6);