Finite Group DatabasebetaFinite Group Databasebeta| order | 6834 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D17×C67⋊C3 |
| unambiguous semidirect product | C17⋊(C2×C67⋊C3) |
| unambiguous semidirect product | (D17×C67)⋊C3 |
| Fitting, socle, derived, Hall | C17×C67 ⋊ C2×C3 |
| Hall | C17×C67⋊C3 ⋊ C2 |
| Hall | D17×C67 ⋊ C3 |
| Sylow | C67 ⋊ C3×D17 |
| Sylow | C17 ⋊ C2×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C67 | C2×C3 |
| LCS | G ▷ C17×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
250 conjugacy classes — view the full character table.
| maximal subgroup of | (C67⋊C3)⋊#595, #595×C67⋊C3, D17×D67⋊C3, … |
| maximal normal subgroup of | (C67⋊C3)⋊#595, #595×C67⋊C3, D17×D67⋊C3, … |
| maximal quotient of | Dic17×C67⋊C3, C2×D17×C67⋊C3, D17×C67⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6834, 11);