Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic689 |
| derived, Hall | C13×C53 ⋊ C3×C4 |
| Hall | C3×C13×C53 ⋊ C4 |
| Hall | C3×C53 ⋊ Dic13 |
| Sylow | C53 ⋊ C3×Dic13 |
| Hall | C3×C13 ⋊ Dic53 |
| Sylow | C13 ⋊ C3×Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D689 |
| commutator, hypocenter | C13×C53 | C3×C4 |
| Frattini | C2 | C3×D689 |
| Fitting, socle | C2×C3×C13×C53 | C2 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
2076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic689, Dic689⋊C9, C3×Dic689⋊C3, … |
| maximal normal subgroup of | C9×Dic689, Dic689⋊C9, C3×Dic689⋊C3, … |
| maximal quotient of | C9×Dic689, C3×Dic2067, C32×Dic689 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 6);