Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×C19×3−1+2 ⋊ C3 |
| Sylow | C19 ⋊ C9⋊H(3,𝔽3) |
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|b^3=d,b^a=bd,c^a=ce,f^c=f^7249 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×C9⋊H(3,𝔽3), C3×#17987422, #28355959, … |
| maximal normal subgroup of | C19⋊C3×C9⋊H(3,𝔽3), C3×#17987422, #28355959, … |
| maximal quotient of | #28353506, #28353529, #28353533, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 183);