Finite Group DatabasebetaFinite Group Databasebeta| order | 16530 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C29 | D19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C29 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C29 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2755 |
1305 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D29×D19⋊C3, D5×C29×D19⋊C3, D19⋊C3×D145, … |
| maximal normal subgroup of | C5×D29×D19⋊C3, D5×C29×D19⋊C3, D19⋊C3×D145, … |
| maximal quotient of | C5×C29×(C19⋊C3)⋊C4, C2×C5×C29×D19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16530, 19);