Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1155 |
| unambiguous semidirect product | C3⋊(C7×D385) |
| unambiguous semidirect product | C5⋊(C7×D231) |
| unambiguous semidirect product | C7⋊(C7×D165) |
| unambiguous semidirect product | C11⋊(C7×D105) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1155 |
| commutator, cosocle, hypocenter | C3×C5×C7×C11 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C11 | C2 |
| LCS | G ▷ C3×C5×C7×C11 | |
| UCS | C1 ◁ C7 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2310 |
4053 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D11×D105, C7×D7×D165, C7×D15×D77, … |
| maximal normal subgroup of | C7×D11×D105, C7×D7×D165, C7×D15×D77, … |
| maximal quotient of | C7×Dic1155, C2×C7×D1155 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 118);