Finite Group DatabasebetaFinite Group Databasebeta| order | 5964 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D497 |
| unambiguous semidirect product | (D3×C7)⋊D71 |
| unambiguous semidirect product | (D3×C71)⋊D7 |
| Fitting, socle, derived, Hall | C3×C7×C71 ⋊ C22 |
| Hall | C7×C71 ⋊ C2×D3 |
| Hall | C3×C71 ⋊ C2×D7 |
| Sylow | C71 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D71 |
| Sylow | C7 ⋊ D3×D71 |
| Sylow | C3 ⋊ C2×D497 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C71 | C22 |
| LCS | G ▷ C3×C7×C71 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
750 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D497, D3×ΓL(1,𝔽8)⋊D71, C3×D3×D497, … |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)⋊D71, C3×D3×D497, D3×C7⋊(D71⋊C5), … |
| maximal quotient of | D9×D497, C3×D3×D497, C3⋊D3×D497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5964, 33);