Finite Group DatabasebetaFinite Group Databasebeta| order | 6396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D39×D41 |
| unambiguous semidirect product | (C3×D41)⋊D13 |
| unambiguous semidirect product | (C13×D41)⋊D3 |
| Fitting, socle, derived, Hall | C3×C13×C41 ⋊ C22 |
| Hall | C13×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×D13 |
| Sylow | C41 ⋊ C2×D39 |
| Hall | C3×C13 ⋊ C2×D41 |
| Sylow | C13 ⋊ D3×D41 |
| 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.
462 conjugacy classes — view the full character table.
| maximal subgroup of | D41×D117, D41×C3⋊(D13⋊C3), C3×D39×D41, … |
| maximal normal subgroup of | D41×C3⋊(D13⋊C3), C3×D39×D41, D39×D41⋊C5, … |
| maximal quotient of | D41×D117, C3×D39×D41, D41×C3⋊D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6396, 38);