Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C11⋊#64422) |
| unambiguous semidirect product | C11⋊(C5⋊#64422) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C11 | C2×C3 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2310 |
Polycyclic presentation:
2,3,5,7^2,11|c^a=c^4,d^a=d^6,f^a=f^10,d^b=d^2,e^b=e^4530 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C5⋊#64422, D55×#64422, D5×C11⋊#64422, … |
| maximal normal subgroup of | D11×C5⋊#64422, D55×#64422, D5×C11⋊#64422, … |
| maximal quotient of | C11⋊#15668737, C2×C5⋊(C11⋊#64422) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 101);