Finite Group DatabasebetaFinite Group Databasebeta| order | 6834 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D67⋊C3) |
| unambiguous semidirect product | (C67⋊C3)⋊D17 |
| unambiguous semidirect product | D1139⋊C3 |
| Fitting, socle, derived, Hall | C17×C67 ⋊ C2×C3 |
| Hall | C17×C67⋊C3 ⋊ C2 |
| Hall | D1139 ⋊ C3 |
| Hall | C67⋊C3 ⋊ D17 |
| Sylow | C67 ⋊ C3×D17 |
| Sylow | C17 ⋊ D67⋊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.
Polycyclic presentation:
2,3,17,67|c^a=c^16,d^a=d^66,d^b=d^37217 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6834, 12);