Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#16813401 |
| derived, Hall | C7×C43 ⋊ C32×C4 |
| Hall | C3×#11744749 ⋊ C4 |
| Hall | C7×Dic43 ⋊ C32 |
| Hall | Dic43 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C43 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×(C43⋊C3)⋊C4 |
72 conjugacy classes of subgroups.
354 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 102);