Finite Group DatabasebetaFinite Group Databasebeta| order | 8274 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D197⋊C7) |
| unambiguous semidirect product | D591⋊C7 |
| unambiguous semidirect product | (C197⋊C7)⋊D3 |
| Fitting, socle, derived, Hall | C3×C197 ⋊ C2×C7 |
| Hall | C3×C197⋊C7 ⋊ C2 |
| Hall | C197⋊C7 ⋊ D3 |
| Hall | D591 ⋊ C7 |
| Sylow | C197 ⋊ D3×C7 |
| Sylow | C3 ⋊ D197⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C197 | C2×C7 |
| LCS | G ▷ C3×C197 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,197|b^a=b^2,d^a=d^196,d^c=d^10463 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8274, 13);