Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C19×C27 ⋊ C9 |
| Sylow | C19 ⋊ #6864 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C3×#4296 |
| commutator, socle | C3×C19 | C92 |
| Fitting | C19×C27 | C9 |
| prime radical | C3×C19⋊C3 | C3×C9 |
| cosocle | C9×C19⋊C3 | C32 |
| hypercenter | C27 | #4296 |
| hypocenter | C19 | #6864 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C9 ◁ C27 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|a^3=c,b^3=d,c^3=e,b^a=be,f^b=f^4,f^d=f^7153 conjugacy classes — view the full character table.
| maximal subgroup of | #28356756, #28356758, #28356760, … |
| maximal normal subgroup of | #28356756, #28356758, #28356760, … |
| maximal quotient of | #28356672, #10587020⋊C27, (C3×#4296)⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 314);