Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C3⋊#6157 |
| unambiguous semidirect product | C3⋊(C13×#6157) |
| Fitting, socle, Hall | C3×C13×C53 ⋊ C4 |
| derived, Hall | C3×C53 ⋊ C4×C13 |
| Hall | C13×C53 ⋊ Dic3 |
| Sylow | C53 ⋊ Dic3×C13 |
| Hall | C3×C13 ⋊ #6157 |
| Sylow | C3 ⋊ C13×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊#6157 |
| commutator, hypocenter | C3×C53 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C53 | C4 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
585 conjugacy classes — view the full character table.
| maximal subgroup of | C13×C9⋊#6157, C13⋊C3×C3⋊#6157, C3×C13×C3⋊#6157, … |
| maximal normal subgroup of | C13⋊C3×C3⋊#6157, C3×C13×C3⋊#6157 |
| maximal quotient of | C13×C9⋊#6157, C3×C13×C3⋊#6157, C13×C3⋊(C3⋊#6157) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 43);