Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D689 |
| unambiguous semidirect product | (D3×C13)⋊D53 |
| unambiguous semidirect product | (D3×C53)⋊D13 |
| Fitting, socle, derived, Hall | C3×C13×C53 ⋊ C22 |
| Hall | C13×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×D13 |
| Sylow | C53 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×D53 |
| Sylow | C13 ⋊ D3×D53 |
| Sylow | C3 ⋊ C2×D689 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C53 | C22 |
| LCS | G ▷ C3×C13×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D689, D3×(C13⋊C3)⋊D53, C3×D3×D689, … |
| maximal normal subgroup of | D3×(C13⋊C3)⋊D53, C3×D3×D689 |
| maximal quotient of | D9×D689, C3×D3×D689, D3×D2067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 53);