Finite Group DatabasebetaFinite Group Databasebeta| order | 6396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D123 |
| unambiguous semidirect product | (C3×D13)⋊D41 |
| unambiguous semidirect product | (D13×C41)⋊D3 |
| Fitting, socle, derived, Hall | C3×C13×C41 ⋊ C22 |
| Hall | C13×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×D13 |
| Sylow | C41 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×D41 |
| Sylow | C13 ⋊ C2×D123 |
| Sylow | C3 ⋊ D13×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C41 | C22 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
504 conjugacy classes — view the full character table.
| maximal subgroup of | D13×D369, D13⋊C3×D123, C3×D13×D123, … |
| maximal normal subgroup of | D13⋊C3×D123, C3×D13×D123, D13×C3⋊(D41⋊C5), … |
| maximal quotient of | D13×D369, C3×D13×D123, D13×C3⋊D123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6396, 40);