Finite Group DatabasebetaFinite Group Databasebeta| order | 16530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2755 |
| unambiguous semidirect product | C5⋊(C3×D551) |
| unambiguous semidirect product | C29⋊(C3×D95) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2755 |
| commutator, cosocle, hypocenter | C5×C19×C29 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C19×C29 | C2 |
| LCS | G ▷ C5×C19×C29 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8265 |
4137 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D29×D95, C3×D19×D145, C3×D5×D551, … |
| maximal normal subgroup of | C3×D29×D95, C3×D19×D145, C3×D5×D551, … |
| maximal quotient of | C3×Dic2755, C2×C3×D2755 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16530, 9);