Finite Group DatabasebetaFinite Group Databasebeta| order | 8214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C1369⋊C3 |
| unambiguous semidirect product | (C2×C1369)⋊C3 |
| Fitting, Hall | C2×C1369 ⋊ C3 |
| derived, Sylow | C1369 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C1369⋊C3 |
| commutator, hypocenter | C1369 | C2×C3 |
| Frattini | C37 | C2×C37⋊C3 |
| Fitting | C2×C1369 | C3 |
| socle | C2×C37 | C37⋊C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
918 conjugacy classes — view the full character table.
| maximal subgroup of | Dic1369⋊C3, C4×C1369⋊C3, C2×D1369⋊C3, … |
| maximal normal subgroup of | Dic1369⋊C3, C4×C1369⋊C3, C2×D1369⋊C3, … |
| maximal quotient of | C4×C1369⋊C3, C22×C1369⋊C3, C2×#27134454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8214, 3);