Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D9×D19 |
| unambiguous semidirect product | (D9×C19)⋊(C2×C7) |
| unambiguous semidirect product | (C9×D19)⋊(C2×C7) |
| unambiguous semidirect product | D171⋊(C2×C7) |
| Fitting, Hall | C7×C9×C19 ⋊ C22 |
| derived, Hall | C9×C19 ⋊ C22×C7 |
| Hall | C7×C19 ⋊ C2×D9 |
| Hall | C7×C9 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C7×D9 |
| Sylow | C9 ⋊ C2×C7×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D9×D19 |
| commutator, cosocle, hypocenter | C9×C19 | C22×C7 |
| Frattini | C3 | D3×C7×D19 |
| Fitting | C7×C9×C19 | C22 |
| socle | C3×C7×C19 | C2×D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1197 |
462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D9×D19, C7×D19×D45, C7×D9×D95, … |
| maximal normal subgroup of | C5×C7×D9×D19, D9×D19×C49, C72×D9×D19 |
| maximal quotient of | C5×C7×D9×D19, C7×D19×D45, C7×D9×D95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 43);