Finite Group DatabasebetaFinite Group Databasebeta| order | 6834 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D51 |
| unambiguous semidirect product | C3⋊(D17×C67) |
| unambiguous semidirect product | C17⋊(D3×C67) |
| Fitting, socle, Hall | C3×C17×C67 ⋊ C2 |
| derived, Hall | C3×C17 ⋊ C2×C67 |
| Hall | C17×C67 ⋊ D3 |
| Hall | C3×C67 ⋊ D17 |
| Sylow | C17 ⋊ D3×C67 |
| Sylow | C3 ⋊ D17×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D51 |
| commutator, hypocenter | C3×C17 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C67 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C67 | |
16 conjugacy classes of subgroups.
1809 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D67, D3×D17×C67, D51⋊D67, … |
| maximal normal subgroup of | D51×D67, D3×D17×C67, D51⋊D67, … |
| maximal quotient of | C67×Dic51, C2×C67×D51, C67×D153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6834, 8);