Finite Group DatabasebetaFinite Group Databasebeta| order | 6132 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#64408⋊C3 |
| unambiguous semidirect product | #64408⋊(C3×C7) |
| Fitting, socle, Hall | C7×C73 ⋊ C3×C4 |
| derived, Sylow | C73 ⋊ C3×C4×C7 |
| Hall | C7×#64408 ⋊ C3 |
| Hall | C7×C73⋊C3 ⋊ C4 |
| Hall | #64408 ⋊ C3×C7 |
| Hall | C73⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #64408⋊C3 |
| commutator, hypocenter | C73 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C73 | C3×C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
126 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14581496, #32913827, #32913828, … |
| maximal normal subgroup of | C7×#14581496, #32913827, #32913828, … |
| maximal quotient of | C7×#14581472, C3×C7×#64408⋊C3, C7×C3⋊(#64408⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6132, 26);