Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C4×C13⋊C3×C53 |
| unambiguous semidirect product | (C4×C13)⋊(C3×C53) |
| unambiguous semidirect product | (C4×C13×C53)⋊C3 |
| Fitting, Hall | C4×C13×C53 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C4×C53 |
| Hall | C13×C53 ⋊ C3×C4 |
| Hall | C4×C13 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C53 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C4×C53 |
| Frattini | C2 | C2×C13⋊C3×C53 |
| Fitting | C4×C13×C53 | C3 |
| socle | C2×C13×C53 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C4×C53 | |
24 conjugacy classes of subgroups.
1484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×C13⋊C3×C53, C3×C4×C13⋊C3×C53 |
| maximal normal subgroup of | C3×C4×C13⋊C3×C53 |
| maximal quotient of | C4×C53×C13⋊C9, Dic3×C13⋊C3×C53, C3×C4×C13⋊C3×C53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 3);