Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Fitting | C19×#737 ⋊ C3 |
| Sylow | C19 ⋊ 3−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C33×C19⋊C3 |
| commutator, socle, cosocle | C3×C19 | C34 |
| Fitting | C19×#737 | C3 |
| prime radical | H(3,𝔽3)×C19⋊C3 | C3 |
| hypercenter | #737 | C19⋊C3 |
| hypocenter | C19 | 3−1+4 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ #737 | |
460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|a^3=e,b^a=be,d^a=de,c^b=ce,f^d=f^7281 conjugacy classes — view the full character table.
| maximal subgroup of | #28356617, #28356622, #28356627, … |
| maximal normal subgroup of | #28356617, #28356622, #28356627, … |
| maximal quotient of | #28355922, #28355925, #28355926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 305);