Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×D55 |
| unambiguous semidirect product | C5⋊(C3×C72×D11) |
| unambiguous semidirect product | C11⋊(C3×C72×D5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | D55 |
| commutator, cosocle, hypocenter | C5×C11 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C11 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C3×C72 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8085 |
4263 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C72×D5×D11, C3×C7×D7×D55, C3×C7×D35⋊D11, … |
| maximal normal subgroup of | C3×C72×D5×D11, C3×C7×D7×D55, C3×C7×D35⋊D11, … |
| maximal quotient of | C3×C72×Dic55, C2×C3×C72×D55 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 132);