Finite Group DatabasebetaFinite Group Databasebeta| order | 6834 |
| isoclinism | isoclinic class of D201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D201 |
| unambiguous semidirect product | C3⋊(C17×D67) |
| unambiguous semidirect product | C67⋊(D3×C17) |
| Fitting, socle, Hall | C3×C17×C67 ⋊ C2 |
| derived, Hall | C3×C67 ⋊ C2×C17 |
| Hall | C17×C67 ⋊ D3 |
| Sylow | C67 ⋊ D3×C17 |
| Hall | C3×C17 ⋊ D67 |
| Sylow | C3 ⋊ C17×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D201 |
| commutator, hypocenter | C3×C67 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C67 | C2 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
1734 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C17×D67, D17×D201, D51⋊D67, … |
| maximal normal subgroup of | D3×C17×D67, D17×D201, D51⋊D67, … |
| maximal quotient of | C17×Dic201, C2×C17×D201, C17×D603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6834, 7);