Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#11924776 |
| derived, Hall | C22×C7×C19 ⋊ C9 |
| Hall | C7×C19 ⋊ C22⋊C9 |
| Hall | C22×C19 ⋊ C7⋊C9 |
| Hall | C22×C7 ⋊ #4294 |
| Sylow | C19 ⋊ C22⋊(C7⋊C9) |
| Sylow | C7 ⋊ C22⋊#4294 |
| Sylow | C22 ⋊ #11924776 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊#87704 |
| commutator, hypocenter | C22×C7×C19 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C7×C19 | C3 |
| LCS | G ▷ C22×C7×C19 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2394 |
Polycyclic presentation:
3,2^2,7,19,3|a^3=f,b^a=c,c^a=bc,d^a=d^4,e^a=e^11540 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C22⋊#11924776, C22⋊#22552692, C22⋊#22552712, … |
| maximal normal subgroup of | C5×C22⋊#11924776, C7×C22⋊#11924776 |
| maximal quotient of | C5×C22⋊#11924776, C22⋊#22552692, C22⋊#22552712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 56);