Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C19×H(3,𝔽3) ⋊ C3 |
| Sylow | C19 ⋊ #6856 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|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×#6856, C3×#17987309, #28353697, … |
| maximal normal subgroup of | C19⋊C3×#6856, C3×#17987309, #28353697, … |
| maximal quotient of | #28353159, #28353160, #28353166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 70);