Finite Group DatabasebetaFinite Group Databasebeta| order | 9492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C113⋊C7 |
| unambiguous semidirect product | C3⋊(C22×C113⋊C7) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C113⋊C7) |
| unambiguous semidirect product | (C2×D3×C113)⋊C7 |
| Fitting, socle | C2×C3×C113 ⋊ C2×C7 |
| derived, Hall | C3×C113 ⋊ C22×C7 |
| Hall | C3×C113⋊C7 ⋊ C22 |
| Hall | C2×D3×C113 ⋊ C7 |
| Sylow | C113 ⋊ C2×D3×C7 |
| Sylow | C3 ⋊ C22×C113⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C113⋊C7 |
| commutator, cosocle, hypocenter | C3×C113 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C113 | C2×C7 |
| LCS | G ▷ C3×C113 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
138 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×C113⋊C7, D32×C113⋊C7, C2×C3×D3×C113⋊C7, … |
| maximal normal subgroup of | C2×C3×D3×C113⋊C7 |
| maximal quotient of | C2×D9×C113⋊C7, D32×C113⋊C7, C2×C3×D3×C113⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9492, 24);