Finite Group DatabasebetaFinite Group Databasebeta| order | 6834 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×D67 |
| Fitting, socle, Hall | C3×C17×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C3×C17 |
| Hall | C17×C67 ⋊ C2×C3 |
| Hall | C3×C67 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | D67 |
| commutator, hypocenter | C67 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C17 | |
16 conjugacy classes of subgroups.
1785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D17×D67, D3×C17×D67, D51×D67, … |
| maximal normal subgroup of | C3×D17×D67, D3×C17×D67, D51×D67, … |
| maximal quotient of | C3×C17×Dic67, C2×C3×C17×D67, C9×C17×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6834, 3);