Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11716328⋊D3 |
| Fitting, socle, derived | C3×C7×C19 ⋊ C22×C3 |
| Hall | C3×#87705 ⋊ C22 |
| Hall | C7×C19 ⋊ C2×C3×D3 |
| Sylow | C19 ⋊ D3×AGL(1,𝔽7) |
| 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 |
Polycyclic presentation:
2^2,3^2,7,19|e^a=e^6,f^a=f^18,d^b=d^2,e^b=e^6,e^c=e^2,f^c=f^1157 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#11716328⋊D3, #11716328⋊D15, #37561380, … |
| maximal normal subgroup of | C5×#11716328⋊D3, C7×#11716328⋊D3 |
| maximal quotient of | C5×#11716328⋊D3, #11716328⋊D15, #37561380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 156);