Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C19 ⋊ #6880 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|a^3=e,b^3=d^2e,c^3=e^2,b^a=bc,c^a=cd,d^a=de,f^b=f^7137 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#6880, C3×#17987375, #28355739, … |
| maximal normal subgroup of | C19⋊C3×#6880, C3×#17987375, #28355739, … |
| maximal quotient of | #28353264, #28353268, #28353311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 136);