Finite Group DatabasebetaFinite Group Databasebeta| order | 6468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽7)×D77 |
| unambiguous semidirect product | D7⋊(C3×D77) |
| unambiguous semidirect product | (C7×AGL(1,𝔽7))⋊D11 |
| unambiguous semidirect product | (C11×AGL(1,𝔽7))⋊D7 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C22×C3 |
| Hall | D7×D77 ⋊ C3 |
| Hall | C7×C11×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×D11 |
| Sylow | C72 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ D7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C11 | C22×C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6468, 82);