Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting | C19×C9⋊C9 ⋊ C3 |
| Sylow | C19 ⋊ #6898 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C19⋊C3 |
| commutator, socle, cosocle | C32×C19 | C33 |
| Fitting | C19×C9⋊C9 | C3 |
| prime radical | C32×C19⋊C3 | C32 |
| hypercenter | C9⋊C9 | C19⋊C3 |
| hypocenter | C19 | #6898 |
| LCS | G ▷ C32×C19 ▷ C19 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
100 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 44 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=e,c^3=d^2,b^a=bd,c^a=ce,f^a=f^11,f^c=f^7249 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#6898, C3×#17987459, #28356015, … |
| maximal normal subgroup of | C19⋊C3×#6898, C3×#17987459, #28356015, … |
| maximal quotient of | #28353520, #28353542, #28353543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 220);