Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×ΓL(1,𝔽8)⋊Dic61 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C7×Dic61) |
| derived | C7×C61 ⋊ C3×C4×C7 |
| Hall | C7×Dic427 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C61 ⋊ C4 |
| Hall | C72×C61 ⋊ C3×C4 |
| Hall | C7×ΓL(1,𝔽8) ⋊ Dic61 |
| Sylow | C61 ⋊ C7×ΓL(1,𝔽8)⋊C4 |
| Sylow | C72 ⋊ C3×Dic61 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5124 |
2198 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 84);