Finite Group DatabasebetaFinite Group Databasebeta| order | 7068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D93 |
| unambiguous semidirect product | (C3×D19)⋊D31 |
| unambiguous semidirect product | (C31×D19)⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C31 ⋊ C22 |
| Hall | C19×C31 ⋊ C2×D3 |
| Hall | C3×C31 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D31 |
| Sylow | C31 ⋊ D3×D19 |
| Sylow | C19 ⋊ C2×D93 |
| Sylow | C3 ⋊ D19×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C31 | C22 |
| LCS | G ▷ C3×C19×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
528 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D279, #16812972⋊D3, #16812971⋊D3, … |
| maximal normal subgroup of | #16812972⋊D3, #16812971⋊D3, D19⋊C3×D93, … |
| maximal quotient of | D19×D279, C3×D19×D93, D57×D93, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7068, 46);