Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×Dic13⋊C3 |
| unambiguous semidirect product | Dic13⋊(C3×C53) |
| unambiguous semidirect product | (Dic13×C53)⋊C3 |
| derived, Sylow | C13 ⋊ C3×C4×C53 |
| Hall | Dic13×C53 ⋊ C3 |
| Hall | C13⋊C3×C53 ⋊ C4 |
| Hall | C13×C53 ⋊ C3×C4 |
| Hall | Dic13 ⋊ C3×C53 |
| Hall | C13⋊C3 ⋊ C4×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D13⋊C3 |
| commutator, hypocenter | C13 | C3×C4×C53 |
| Frattini | C2 | C53×D13⋊C3 |
| Fitting, socle | C2×C13×C53 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C53 | |
24 conjugacy classes of subgroups.
848 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C53×Dic13⋊C3, C53×C3⋊(Dic13⋊C3) |
| maximal normal subgroup of | C3×C53×Dic13⋊C3 |
| maximal quotient of | C53×Dic13⋊C9, C3×C53×Dic13⋊C3, C53×C3⋊(Dic13⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 15);