Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C36 |
| unambiguous semidirect product | (C3×C19⋊C3)⋊H(3,𝔽3) |
| Fitting | C3×C19×H(3,𝔽3) ⋊ C3 |
| Sylow | C19 ⋊ C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C19⋊C3 |
| commutator, socle, cosocle | C32×C19 | C33 |
| Fitting | C3×C19×H(3,𝔽3) | C3 |
| hypercenter | C3×H(3,𝔽3) | C19⋊C3 |
| hypocenter | C19 | C32⋊H(3,𝔽3) |
| LCS | G ▷ C32×C19 ▷ C19 | |
| UCS | C1 ◁ C32 ◁ C3×H(3,𝔽3) | |
378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|b^a=bd,c^a=ce,f^c=f^7249 conjugacy classes — view the full character table.
| maximal subgroup of | #28353773, #28353774, #28353783, … |
| maximal normal subgroup of | #28353773, #28353774, #28353783, … |
| maximal quotient of | #28353504, #28353529, #28353530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 177);