Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊(D49⋊C3) |
| unambiguous semidirect product | (C49⋊C3)⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C11⋊(D49⋊C3))⋊C5 |
| unambiguous semidirect product | (C49⋊AGL(1,𝔽11))⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C49 | C2×C3×C5 |
| Frattini | C7 | ΓL(1,𝔽8)⋊AGL(1,𝔽11) |
| socle | C7×C11 | C5×AGL(1,𝔽7) |
| LCS | G ▷ C11×C49 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 539 |
Polycyclic presentation:
2,3,5,7,11,7|d^7=f^6,d^a=d^6f,e^a=e^10,f^a=f^6,d^b=d^2f^3,f^b=f^2,e^c=e^489 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×D49⋊C3, C2×(C11⋊C5)⋊(D49⋊C3) |
| maximal normal subgroup of | AGL(1,𝔽11)×D49⋊C3, C2×(C11⋊C5)⋊(D49⋊C3) |
| maximal quotient of | (C11⋊C5)⋊((C49⋊C3)⋊C4), C2×(C11⋊C5)⋊(D49⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 36);