Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C49⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | C49⋊(C3⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊D147 |
| unambiguous semidirect product | D1617⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C11×C49 | C2×C5 |
| Frattini | C7 | C3⋊(C7⋊AGL(1,𝔽11)) |
| socle | C3×C7×C11 | C5×D7 |
| LCS | G ▷ C3×C11×C49 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1617 |
Polycyclic presentation:
2,3,5,7,11,7|d^7=f^6,b^a=b^2,d^a=d^6f,e^a=e^10,f^a=f^6,e^c=e^4522 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 26);