Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C5×C72×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C72 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C3×C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C11 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C5×C72 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8085 |
5145 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C7×D7×D11, C3×C5×D11×C7⋊D7, C3×C72×D5×D11, … |
| maximal normal subgroup of | C3×C5×C7×D7×D11, C3×C5×D11×C7⋊D7, C3×C72×D5×D11, … |
| maximal quotient of | C3×C5×C72×Dic11, C2×C3×C5×C72×D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 138);