Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C19 ⋊ #6903 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×#4296 |
| commutator, socle | C3×C19 | C32×C9 |
| Fitting, prime radical | C19×H(3,𝔽3) | C9 |
| cosocle | #4294 | C33 |
| hypercenter | H(3,𝔽3) | #4296 |
| hypocenter | C19 | #6903 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=d,d^3=e,f^a=f^4,c^b=ce,f^d=f^7121 conjugacy classes — view the full character table.
| maximal subgroup of | #28356998, #28356999, #28357001, … |
| maximal normal subgroup of | #28356998, #28356999, #28357001, … |
| maximal quotient of | #28356881, #28356891, #28356946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 359);