Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D21⋊D11 |
| unambiguous semidirect product | D21⋊(C11×D11) |
| unambiguous semidirect product | D33⋊(C11×D7) |
| unambiguous semidirect product | D77⋊(D3×C11) |
| Fitting, socle, Hall | C3×C7×C112 ⋊ C22 |
| derived | C3×C7×C11 ⋊ C22×C11 |
| Hall | C7×C112 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D7 |
| Sylow | C112 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×C11×D11 |
| Sylow | C7 ⋊ D3×C11×D11 |
| Sylow | C3 ⋊ C11×D7×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D21⋊D11 |
| commutator, cosocle, hypocenter | C3×C7×C11 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C112 | C22 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C11 | |
120 conjugacy classes of subgroups.
825 conjugacy classes — view the full character table.
| maximal subgroup of | C11×D63⋊D11, C11×D33⋊AGL(1,𝔽7), D21⋊#10624391, … |
| maximal normal subgroup of | C11×D33⋊AGL(1,𝔽7), C3×C11×D21⋊D11 |
| maximal quotient of | C11×D63⋊D11, C3×C11×D21⋊D11, C11×D33⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 116);