Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C3×C19×3−1+2 ⋊ C3 |
| Sylow | C19 ⋊ #6857 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=d,b^a=bc,c^a=cd,c^b=ce,f^b=f^7233 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#6857, C3×#17987311, #28353697, … |
| maximal normal subgroup of | C19⋊C3×#6857, C3×#17987311, #28353697, … |
| maximal quotient of | #28353159, #28353163, #28353167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 72);