Finite Group DatabasebetaFinite Group Databasebeta| order | 6468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×#64418 |
| Fitting, socle, Hall | C72×C11 ⋊ C2×D3 |
| derived, Hall | C11×#3862 ⋊ C22 |
| Hall | #3862 ⋊ C2×D11 |
| Sylow | C72 ⋊ D3×D11 |
| Sylow | C11 ⋊ C2×#64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C11×#3862 | C22 |
| Fitting, socle | C72×C11 | C2×D3 |
| LCS | G ▷ C11×#3862 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6468, 90);