Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C3⋊#261 |
| unambiguous semidirect product | C3⋊(#261×C53) |
| Fitting, socle, Hall | C3×C13×C53 ⋊ C4 |
| derived, Hall | C3×C13 ⋊ C4×C53 |
| Hall | C13×C53 ⋊ Dic3 |
| Hall | C3×C53 ⋊ #261 |
| Sylow | C13 ⋊ Dic3×C53 |
| Sylow | C3 ⋊ #261×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C4×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C53 | C4 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C53 | |
24 conjugacy classes of subgroups.
795 conjugacy classes — view the full character table.
| maximal subgroup of | C53×C9⋊#261, C53×C3⋊AGL(1,𝔽13), C3×C53×C3⋊#261, … |
| maximal normal subgroup of | C53×C3⋊AGL(1,𝔽13), C3×C53×C3⋊#261 |
| maximal quotient of | C53×C9⋊#261, C3×C53×C3⋊#261, C53×C3⋊(C3⋊#261) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 45);