Finite Group DatabasebetaFinite Group Databasebeta| order | 9492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D339 |
| unambiguous semidirect product | (C3×D7)⋊D113 |
| unambiguous semidirect product | (D7×C113)⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C113 ⋊ C22 |
| Hall | C7×C113 ⋊ C2×D3 |
| Hall | C3×C113 ⋊ C2×D7 |
| Sylow | C113 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D113 |
| Sylow | C7 ⋊ C2×D339 |
| Sylow | C3 ⋊ D7×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C113 | C22 |
| LCS | G ▷ C3×C7×C113 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
855 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D1017, AGL(1,𝔽7)×D339, C3×D7×D339, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D339, C3×D7×D339 |
| maximal quotient of | D7×D1017, C3×D7×D339, D21×D339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9492, 40);