Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C19×C9⋊C9 ⋊ C3 |
| Sylow | C19 ⋊ #6894 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C19⋊C3 |
| commutator, socle, cosocle | C32×C19 | C33 |
| Fitting | C19×C9⋊C9 | C3 |
| prime radical | C32×C19⋊C3 | C32 |
| hypercenter | C9⋊C9 | C19⋊C3 |
| hypocenter | C19 | #6894 |
| LCS | G ▷ C32×C19 ▷ C19 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=e,b^3=d,b^a=bd,c^a=ce,f^c=f^7249 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#6894, C3×#17987433, #28355981, … |
| maximal normal subgroup of | C19⋊C3×#6894, C3×#17987433, #28355981, … |
| maximal quotient of | #28353506, #28353536, #28353550, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 194);