Finite Group DatabasebetaFinite Group Databasebeta| order | 6996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D159 |
| unambiguous semidirect product | (C3×D11)⋊D53 |
| unambiguous semidirect product | (D11×C53)⋊D3 |
| Fitting, socle, derived, Hall | C3×C11×C53 ⋊ C22 |
| Hall | C11×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×D11 |
| Sylow | C53 ⋊ D3×D11 |
| Hall | C3×C11 ⋊ C2×D53 |
| Sylow | C11 ⋊ C2×D159 |
| Sylow | C3 ⋊ D11×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C53 | C22 |
| LCS | G ▷ C3×C11×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
567 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D477, C3×D11×D159, D33×D159, … |
| maximal normal subgroup of | C3×D11×D159, AGL(1,𝔽11)×D159, C5×D11×D159 |
| maximal quotient of | D11×D477, C3×D11×D159, D33×D159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6996, 18);