Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×(C13⋊C3)⋊D53 |
| unambiguous semidirect product | (C2×C13⋊C3)⋊D53 |
| unambiguous semidirect product | (C2×C53)⋊(D13⋊C3) |
| unambiguous semidirect product | (C2×D689)⋊C3 |
| Fitting, socle | C2×C13×C53 ⋊ C2×C3 |
| derived, Hall | C13×C53 ⋊ C22×C3 |
| Hall | C2×D689 ⋊ C3 |
| Hall | C13⋊C3×C53 ⋊ C22 |
| Sylow | C53 ⋊ C2×D13⋊C3 |
| Hall | C13⋊C3 ⋊ C2×D53 |
| Sylow | C13 ⋊ C2×C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C13⋊C3)⋊D53 |
| commutator, hypocenter | C13×C53 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C53 | C2×C3 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(C13⋊C3)⋊D53, C2×C3×(C13⋊C3)⋊D53, C2×C3⋊((C13⋊C3)⋊D53) |
| maximal normal subgroup of | C2×C3×(C13⋊C3)⋊D53 |
| maximal quotient of | C2×C53⋊(D13⋊C9), D3×(C13⋊C3)⋊D53, C2×C3×(C13⋊C3)⋊D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 34);