Finite Group DatabasebetaFinite Group Databasebeta| order | 6132 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic73⋊C3 |
| unambiguous semidirect product | Dic73⋊(C3×C7) |
| derived, Sylow | C73 ⋊ C3×C4×C7 |
| Hall | C7×Dic73 ⋊ C3 |
| Hall | C7×C73⋊C3 ⋊ C4 |
| Hall | C7×C73 ⋊ C3×C4 |
| Hall | Dic73 ⋊ C3×C7 |
| Hall | C73⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D73⋊C3 |
| commutator, hypocenter | C73 | C3×C4×C7 |
| Frattini | C2 | C7×D73⋊C3 |
| Fitting, socle | C2×C7×C73 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
252 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14581484, #32913767, #32913768, … |
| maximal normal subgroup of | C7×#14581484, #32913767, #32913768, … |
| maximal quotient of | C7×#14581466, C3×C7×Dic73⋊C3, C7×C3⋊(Dic73⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6132, 13);