Finite Group DatabasebetaFinite Group Databasebeta| order | 7068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D3×C31×D19 |
| unambiguous semidirect product | (D3×C19)⋊(C2×C31) |
| unambiguous semidirect product | (C3×D19)⋊(C2×C31) |
| unambiguous semidirect product | D57⋊(C2×C31) |
| Fitting, socle, Hall | C3×C19×C31 ⋊ C22 |
| derived, Hall | C3×C19 ⋊ C22×C31 |
| Hall | C19×C31 ⋊ C2×D3 |
| Hall | C3×C31 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D3×C31 |
| Sylow | C3 ⋊ C2×C31×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×D19 |
| commutator, hypocenter | C3×C19 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C31 | C22 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C31 | |
40 conjugacy classes of subgroups.
1023 conjugacy classes — view the full character table.
| maximal subgroup of | D9×C31×D19, D3×C31×D19⋊C3, D3×#16812972, … |
| maximal normal subgroup of | D3×C31×D19⋊C3, D3×#16812972, D3×#16812971, … |
| maximal quotient of | D9×C31×D19, C3×D3×C31×D19, D3×C31×D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7068, 45);