Finite Group DatabasebetaFinite Group Databasebeta| order | 6132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D7×D73⋊C3 |
| unambiguous semidirect product | D73⋊(C3×D7) |
| unambiguous semidirect product | (C7×D73⋊C3)⋊C2 |
| unambiguous semidirect product | (D7×C73⋊C3)⋊C2 |
| unambiguous semidirect product | ((C73⋊C3)⋊D7)⋊C2 |
| Fitting, socle, derived, Hall | C7×C73 ⋊ C22×C3 |
| Hall | D7×D73 ⋊ C3 |
| Hall | C7×C73⋊C3 ⋊ C22 |
| Hall | C73⋊C3 ⋊ C2×D7 |
| Sylow | C73 ⋊ C2×C3×D7 |
| Sylow | C7 ⋊ C2×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C22×C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6132, 37);