Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D21×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×D21) |
| unambiguous semidirect product | (C3×D19⋊C3)⋊D7 |
| unambiguous semidirect product | (C7×D19⋊C3)⋊D3 |
| Fitting, socle, derived | C3×C7×C19 ⋊ C22×C3 |
| Hall | C3×C7×C19⋊C3 ⋊ C22 |
| Hall | C3×C19⋊C3 ⋊ C2×D7 |
| Hall | C7×C19 ⋊ C2×C3×D3 |
| Sylow | C19 ⋊ C2×C3×D21 |
| Sylow | C7 ⋊ D3×D19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C19 | C22×C3 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 399 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D21×D19⋊C3, D19⋊C3×D105, D21×C5⋊(D19⋊C3), … |
| maximal normal subgroup of | C5×D21×D19⋊C3, C7×D21×D19⋊C3 |
| maximal quotient of | C5×D21×D19⋊C3, D19⋊C3×D105, D21×C5⋊(D19⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 165);