Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D33⋊D11 |
| unambiguous semidirect product | D33⋊(C7×D11) |
| Fitting, socle, Hall | C3×C7×C112 ⋊ C22 |
| derived, Hall | C3×C112 ⋊ C22×C7 |
| Hall | C7×C112 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×D3×C7 |
| Hall | C3×C7 ⋊ D112 |
| Sylow | C3 ⋊ C7×D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D33⋊D11 |
| commutator, cosocle, hypocenter | C3×C112 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C112 | C22 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C7 | |
120 conjugacy classes of subgroups.
777 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14546095⋊C2, C7×D99⋊D11, C7×((C11⋊D11)⋊C3)⋊D3, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×D33⋊D11, C3×C7×D33⋊D11 |
| maximal quotient of | C7×D99⋊D11, C3×C7×D33⋊D11, C7×D33⋊D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 106);