Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C19 ⋊ #6873 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=d,d^3=e^2,b^a=bc,c^a=ce,f^a=f^4,c^b=ce,f^d=f^773 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#17987568, (C19⋊C3)⋊#6873, #28356928, … |
| maximal normal subgroup of | C3×#17987568, (C19⋊C3)⋊#6873, #28356928, … |
| maximal quotient of | H(3,𝔽3)⋊#10587020, #28356685, #28356690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 329);