Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C3×(C19⋊C3)⋊C27 |
| unambiguous semidirect product | (C19⋊C3)⋊(C3×C27) |
| derived, Sylow | C19 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | #4296 |
| commutator, hypocenter | C19 | C32×C27 |
| Frattini | C3 | C32×#4296 |
| Fitting | C3×C9×C19 | C9 |
| socle | C32×C19 | C3×C9 |
| prime radical | C32×C19⋊C3 | C9 |
| cosocle | #4294 | C33 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C9 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C3×#4296)⋊C27, #28356727, #28356730, … |
| maximal normal subgroup of | (C3×#4296)⋊C27, #28356727, #28356730, … |
| maximal quotient of | C3×C9×#10587020, C9×(C19⋊C3)⋊C27, (C19⋊C3)⋊(C32⋊C27), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 354);