Finite Group DatabasebetaFinite Group Databasebeta| order | 8229 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C211⋊C3 |
| unambiguous semidirect product | C211⋊(C3×C13) |
| Fitting, socle, Hall | C13×C211 ⋊ C3 |
| derived, Sylow | C211 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C211⋊C3 |
| commutator, hypocenter | C211 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C211 | C3 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
949 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13×C211⋊C3, C13×D211⋊C3, D13×C211⋊C3, … |
| maximal normal subgroup of | C2×C13×C211⋊C3, C13×D211⋊C3, D13×C211⋊C3, … |
| maximal quotient of | C2×C13×C211⋊C3, C13×C211⋊C9, C3×C13×C211⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8229, 2);