Finite Group DatabasebetaFinite Group Databasebeta| order | 6834 |
| isoclinism | isoclinic class of D67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D67⋊C3 |
| unambiguous semidirect product | D67⋊(C3×C17) |
| unambiguous semidirect product | (C67⋊C3)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D67)⋊C3 |
| Fitting, socle, Hall | C17×C67 ⋊ C2×C3 |
| derived, Sylow | C67 ⋊ C2×C3×C17 |
| Hall | C17×C67⋊C3 ⋊ C2 |
| Hall | C17×D67 ⋊ C3 |
| Hall | C67⋊C3 ⋊ C2×C17 |
| Hall | D67 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D67⋊C3 |
| commutator, hypocenter | C67 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C67 | C2×C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
289 conjugacy classes — view the full character table.
| maximal subgroup of | D17×D67⋊C3, C2×C17×D67⋊C3, C3×C17×D67⋊C3, … |
| maximal normal subgroup of | D17×D67⋊C3, C2×C17×D67⋊C3, C3×C17×D67⋊C3, … |
| maximal quotient of | C17×(C67⋊C3)⋊C4, C2×C17×D67⋊C3, C17×D67⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6834, 10);