Finite Group DatabasebetaFinite Group Databasebeta| order | 6594 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D157⋊C3 |
| unambiguous semidirect product | D157⋊(C3×C7) |
| unambiguous semidirect product | (C157⋊C3)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C157 ⋊ C2×C3 |
| derived, Sylow | C157 ⋊ C2×C3×C7 |
| Hall | C7×C157⋊C3 ⋊ C2 |
| Hall | C7×D157 ⋊ C3 |
| Hall | C157⋊C3 ⋊ C2×C7 |
| Hall | D157 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D157⋊C3 |
| commutator, hypocenter | C157 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C157 | C2×C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
224 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#10597845⋊C3, #27210001, D7×D157⋊C3, … |
| maximal normal subgroup of | C7×#10597845⋊C3, #27210001, D7×D157⋊C3, … |
| maximal quotient of | C7×Dic157⋊C3, C2×C7×D157⋊C3, C7×D157⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6594, 13);