Finite Group DatabasebetaFinite Group Databasebeta| order | 6996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D33×D53 |
| unambiguous semidirect product | (C3×D53)⋊D11 |
| unambiguous semidirect product | (C11×D53)⋊D3 |
| Fitting, socle, derived, Hall | C3×C11×C53 ⋊ C22 |
| Hall | C11×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×D11 |
| Sylow | C53 ⋊ C2×D33 |
| Hall | C3×C11 ⋊ C2×D53 |
| Sylow | C11 ⋊ D3×D53 |
| 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.
504 conjugacy classes — view the full character table.
| maximal subgroup of | D53×D99, C3×D33×D53, D159⋊D33, … |
| maximal normal subgroup of | C3×D33×D53, D53×C3⋊AGL(1,𝔽11), C5×D33×D53 |
| maximal quotient of | D53×D99, C3×D33×D53, D159⋊D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6996, 16);