Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Sylow | C19 ⋊ #6855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C3×C19⋊C3 |
| commutator | C3×C19 | C92 |
| Fitting | C32×C9×C19 | C3 |
| socle, prime radical, cosocle | C33×C19 | C32 |
| hypercenter | C32×C9 | C19⋊C3 |
| hypocenter | C19 | #6855 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C33 ◁ C32×C9 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4617 |
Polycyclic presentation:
3^5,19|a^3=d,b^3=e,b^a=bc,f^b=f^7585 conjugacy classes — view the full character table.
| maximal subgroup of | #28353253, #28353255, #28353256, … |
| maximal normal subgroup of | #28353253, #28353255, #28353256, … |
| maximal quotient of | #28353196, #28353197, #28353198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 69);