Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C11⋊#64418) |
| unambiguous semidirect product | C11⋊(C5⋊#64418) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C11×#3862 | C2 |
| Fitting, socle | C5×C72×C11 | D3 |
| LCS | G ▷ C5×C11×#3862 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 770 |
Polycyclic presentation:
2,3,5,11,7^2|b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^4f,f^a=e^6f^3,e^b=e^2f^6,f^b=f^4533 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C5⋊#64418, D55×#64418, D5×C11⋊#64418, … |
| maximal normal subgroup of | D11×C5⋊#64418, D55×#64418, D5×C11⋊#64418, … |
| maximal quotient of | C11⋊#15668724, C2×C5⋊(C11⋊#64418) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 111);