Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C19×C32⋊C9 ⋊ C3 |
| Sylow | C19 ⋊ C9⋊H(3,𝔽3) |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|b^3=d,b^a=bd,c^a=ce,f^a=f^7,f^b=f^11249 conjugacy classes — view the full character table.
| maximal subgroup of | #28353798, #28353801, #28353804, … |
| maximal normal subgroup of | #28353798, #28353801, #28353804, … |
| maximal quotient of | #28353507, #28353530, #28353535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 189);