Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle, derived, Hall | C22×C43 ⋊ C32×C7 |
| Hall | A4×C43⋊C3 ⋊ C7 |
| Hall | C22×C43⋊C7 ⋊ C32 |
| Hall | C43⋊C7 ⋊ C3×A4 |
| Sylow | C43 ⋊ C3×C7×A4 |
| Sylow | C22 ⋊ C3×(C43⋊C3)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C43 | C32×C7 |
| LCS | G ▷ C22×C43 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
92 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AGL(1,𝔽43), S4×(C43⋊C3)⋊C7, #72269569 |
| maximal normal subgroup of | A4×AGL(1,𝔽43), S4×(C43⋊C3)⋊C7, #72269569 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 140);