Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#11924781 |
| Fitting, socle, Hall | C22×C7×C19 ⋊ C9 |
| derived, Hall | C7×C19 ⋊ C22×C9 |
| Hall | C22×C19 ⋊ C7⋊C9 |
| Hall | C22×C7 ⋊ #4296 |
| Sylow | C19 ⋊ C22×C7⋊C9 |
| Sylow | C7 ⋊ C22×#4296 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11924781 |
| commutator, hypocenter | C7×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C19 | C9 |
| prime radical | C22×C7×C19⋊C3 | C3 |
| cosocle | C7×C19⋊C3 | C22×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 532 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 172);