Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C7×C112 ⋊ C22×C3 |
| derived | C7×C11 ⋊ C22×C3×C11 |
| Hall | C11×D7×D11 ⋊ C3 |
| Hall | C112×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C112 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×C11×D11 |
| Sylow | C7 ⋊ C2×C3×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D11×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7×C11 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112 | C22×C3 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C11 | |
120 conjugacy classes of subgroups.
539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 67);