Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C3×#261×C53 |
| Fitting, socle, Hall | C3×C13×C53 ⋊ C4 |
| derived, Sylow | C13 ⋊ C3×C4×C53 |
| Hall | C13×C53 ⋊ C3×C4 |
| Hall | C3×C13 ⋊ C4×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C53 | #261 |
| commutator, hypocenter | C13 | C3×C4×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C53 | C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C53 | |
24 conjugacy classes of subgroups.
1113 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#261⋊C9, C9×#261×C53, C3×C53×AGL(1,𝔽13), … |
| maximal normal subgroup of | C53×#261⋊C9, C9×#261×C53, C3×C53×AGL(1,𝔽13), … |
| maximal quotient of | C9×#261×C53, C32×#261×C53, C3×C53×C3⋊#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 37);