Finite Group DatabasebetaFinite Group Databasebeta| order | 6396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊D41 |
| unambiguous semidirect product | D123⋊D13 |
| unambiguous semidirect product | D533⋊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 ⋊ 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.
Polycyclic presentation:
2^2,3,13,41|d^a=d^12,e^a=e^40,c^b=c^2,d^b=d^12444 conjugacy classes — view the full character table.
| maximal subgroup of | D117⋊D41, (C3⋊(D13⋊C3))⋊D41, C3×D39⋊D41, … |
| maximal normal subgroup of | (C3⋊(D13⋊C3))⋊D41, C3×D39⋊D41, D39⋊(D41⋊C5), … |
| maximal quotient of | D117⋊D41, C3×D39⋊D41, D533⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6396, 42);