Finite Group DatabasebetaFinite Group Databasebeta| order | 16530 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C5×C29×D57 |
| unambiguous semidirect product | C3⋊(C5×C29×D19) |
| unambiguous semidirect product | C19⋊(C5×D3×C29) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C29 | D57 |
| commutator, cosocle, hypocenter | C3×C19 | C2×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C19×C29 | C2 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C5×C29 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8265 |
4350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D29×D57, C5×D3×C29×D19, C5×D57⋊D29, … |
| maximal normal subgroup of | C5×D29×D57, C5×D3×C29×D19, C5×D57⋊D29, … |
| maximal quotient of | C5×C29×Dic57, C2×C5×C29×D57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16530, 12);