Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| isoclinism | isoclinic class of D219 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D219 |
| unambiguous semidirect product | C3⋊(C3×C13×D73) |
| Fitting, socle, Hall | C32×C13×C73 ⋊ C2 |
| derived | C3×C73 ⋊ C2×C3×C13 |
| Hall | C13×C73 ⋊ C3×D3 |
| Hall | C32×C73 ⋊ C2×C13 |
| Hall | C32×C13 ⋊ D73 |
| Sylow | C73 ⋊ C3×D3×C13 |
| Sylow | C32 ⋊ C13×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D219 |
| commutator, cosocle, hypocenter | C3×C73 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C73 | C2 |
| LCS | G ▷ C3×C73 | |
| UCS | C1 ◁ C3×C13 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5694 |
4329 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C13×D73, C3×D13×D219, C3×D39⋊D73, … |
| maximal normal subgroup of | C3×D3×C13×D73, C3×D13×D219, C3×D39⋊D73, … |
| maximal quotient of | C3×C13×Dic219, C2×C3×C13×D219 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 80);