Finite Group DatabasebetaFinite Group Databasebeta| order | 8274 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C197⋊C7 |
| unambiguous semidirect product | (C2×C197)⋊(C3×C7) |
| unambiguous semidirect product | (C2×C3×C197)⋊C7 |
| Fitting, socle, Hall | C2×C3×C197 ⋊ C7 |
| derived, Sylow | C197 ⋊ C2×C3×C7 |
| Hall | C3×C197 ⋊ C2×C7 |
| Hall | C2×C197 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C197⋊C7 |
| commutator, hypocenter | C197 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C197 | C7 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
210 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C197⋊C7, C3×Dic197⋊C7, Dic3×C197⋊C7, … |
| maximal normal subgroup of | C3×C4×C197⋊C7, C3×Dic197⋊C7, Dic3×C197⋊C7, … |
| maximal quotient of | C3×C4×C197⋊C7, C22×C3×C197⋊C7, C2×C9×C197⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8274, 2);