Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C243 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C19 ⋊ C243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C81 | C19⋊C3 |
| commutator, hypocenter | C19 | C243 |
| Fitting, cosocle | C19×C81 | C3 |
| socle, prime radical | C3×C19 | C81 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C81 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 262 |
| transitive degree | μt(G) = 4617 |
Polycyclic presentation:
3^5,19|a^3=b,b^3=c,c^3=d,d^3=e,f^a=f^7729 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×C243, C3×#17987307, #28353465, … |
| maximal normal subgroup of | C19⋊C3×C243, C3×#17987307, #28353465, … |
| maximal quotient of | #28353141, C3×#17987307 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 68);