Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D63 |
| unambiguous semidirect product | (C7×D19)⋊D9 |
| unambiguous semidirect product | (C9×D19)⋊D7 |
| Fitting, derived, Hall | C7×C9×C19 ⋊ C22 |
| Hall | C9×C19 ⋊ C2×D7 |
| Hall | C7×C19 ⋊ C2×D9 |
| Hall | C7×C9 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D63 |
| Sylow | C9 ⋊ D7×D19 |
| Sylow | C7 ⋊ D9×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C9×C19 | C22 |
| Frattini | C3 | D19×D21 |
| socle | C3×C7×C19 | C2×D3 |
| LCS | G ▷ C7×C9×C19 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1197 |
363 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D19×D63, D19×D315, D63×D95, … |
| maximal normal subgroup of | C5×D19×D63, C7×D19×D63 |
| maximal quotient of | C5×D19×D63, D19×D315, D63×D95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 44);