Finite Group DatabasebetaFinite Group Databasebeta| order | 9492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×#90673⋊C7 |
| unambiguous semidirect product | #90673⋊(C3×C7) |
| unambiguous semidirect product | (C3×#90673)⋊C7 |
| Fitting, socle, Hall | C3×C113 ⋊ C4×C7 |
| derived, Sylow | C113 ⋊ C3×C4×C7 |
| Hall | C3×C113⋊C7 ⋊ C4 |
| Hall | C3×#90673 ⋊ C7 |
| Hall | C113⋊C7 ⋊ C3×C4 |
| Hall | #90673 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #90673⋊C7 |
| commutator, hypocenter | C113 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C113 | C4×C7 |
| prime radical | C3×D113⋊C7 | C2 |
| cosocle | D113 | C2×C3×C7 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
96 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#90673⋊C7, C32×#90673⋊C7, C3×C3⋊(#90673⋊C7) |
| maximal normal subgroup of | C9×#90673⋊C7, C32×#90673⋊C7 |
| maximal quotient of | C9×#90673⋊C7, C32×#90673⋊C7, C3×C3⋊(#90673⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9492, 18);