Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C3×C53 ⋊ C22×C13 |
| Hall | C3×C53⋊C13 ⋊ C22 |
| Hall | C53⋊C13 ⋊ C2×D3 |
| Hall | D3×D53 ⋊ C13 |
| Sylow | C53 ⋊ C2×D3×C13 |
| Sylow | C3 ⋊ C2×D53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C53 | C22×C13 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
84 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D53⋊C13, C3×D3×D53⋊C13, D3×C3⋊(D53⋊C13), … |
| maximal normal subgroup of | C3×D3×D53⋊C13, D3×AGL(1,𝔽53) |
| maximal quotient of | D9×D53⋊C13, C3×D3×D53⋊C13, D3×C3⋊(D53⋊C13), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 20);