Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#13097582 |
| derived, Hall | C7×C19 ⋊ C32×C4 |
| Hall | C3×#87704 ⋊ C4 |
| Hall | C7×Dic19 ⋊ C32 |
| Hall | Dic19 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C19 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×(C19⋊C3)⋊C4 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1596 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×#13097582, C3×#22547614, C3×#22547638, … |
| maximal normal subgroup of | C3×C5×#13097582, C3×C7×#13097582 |
| maximal quotient of | C3×C5×#13097582, C3×#22547614, C3×#22547638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 89);