Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| derived, Hall | C7×C19 ⋊ C32×C4 |
| Hall | ΓL(1,𝔽8)×C19⋊C3 ⋊ C4 |
| Hall | C19×Dic7 ⋊ C32 |
| Hall | Dic7 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ C3×C4×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽7)×C19⋊C3 |
| commutator, hypocenter | C7×C19 | C32×C4 |
| Fitting, socle, cosocle | C2×C7×C19 | C2×C32 |
| prime radical | C2×ΓL(1,𝔽8)×C19⋊C3 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 532 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 72);