Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ #6875 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|a^3=d,b^3=c,c^3=e,b^a=bc,c^a=ce,f^a=f^7,d^b=de^2,f^b=f^11233 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#6875, C3×#17987362, #28354740, … |
| maximal normal subgroup of | C19⋊C3×#6875, C3×#17987362, #28354740, … |
| maximal quotient of | #28353193, #28353222, C3×#17987362 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 123);