Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C361 · Schur multiplier (H2) = C1 |
| direct product | D15×C361 |
| unambiguous semidirect product | C3⋊(D5×C361) |
| unambiguous semidirect product | C5⋊(D3×C361) |
| Fitting, Hall | C3×C5×C361 ⋊ C2 |
| derived, Hall | C3×C5 ⋊ C2×C361 |
| Hall | C5×C361 ⋊ D3 |
| Hall | C3×C361 ⋊ D5 |
| Sylow | C5 ⋊ D3×C361 |
| Sylow | C3 ⋊ D5×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C361 | D15 |
| commutator, hypocenter | C3×C5 | C2×C361 |
| Frattini | C19 | C19×D15 |
| Fitting | C3×C5×C361 | C2 |
| socle, cosocle | C3×C5×C19 | C2×C19 |
| prime radical | C19×D15 | C19 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C361 | |
24 conjugacy classes of subgroups.
3249 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D361, D3×D5×C361, D15⋊D361, … |
| maximal normal subgroup of | D15×D361, D3×D5×C361, D15⋊D361, … |
| maximal quotient of | Dic15×C361, C2×D15×C361, D45×C361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 11);