Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ C81⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C3×#4296 |
| commutator, socle | C3×C19 | C3×C27 |
| Fitting | C19×C27 | C9 |
| prime radical | C3×C19⋊C3 | C27 |
| cosocle | #10587018 | C32 |
| hypercenter | C27 | #4296 |
| hypocenter | C19 | C81⋊C3 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C9 ◁ C27 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=c,c^3=d,d^3=e,b^a=be,f^a=f^16,f^b=f^7,f^c=f^11153 conjugacy classes — view the full character table.
| maximal subgroup of | #28356756, #28356758, #28356760, … |
| maximal normal subgroup of | #28356756, #28356758, #28356760, … |
| maximal quotient of | #28356755, #28356766, #28356827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 345);