Finite Group DatabasebetaFinite Group Databasebeta| order | 6468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C11⋊#64425 |
| unambiguous semidirect product | (C2×C11)⋊#64425 |
| Fitting, socle | C2×C72×C11 ⋊ C2×C3 |
| derived, Hall | C72×C11 ⋊ C22×C3 |
| Hall | C2×C7⋊D77 ⋊ C3 |
| Hall | C11×#3862 ⋊ C22 |
| Hall | #3862 ⋊ C2×D11 |
| Sylow | C72 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ C2×#64425 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊#64425 |
| commutator, hypocenter | C72×C11 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C11 | C2×C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
218 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6468, 101);