Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D39×C73⋊C3 |
| unambiguous semidirect product | C3⋊(D13×C73⋊C3) |
| Fitting, socle, derived | C3×C13×C73 ⋊ C2×C3 |
| Hall | C3×C13×C73⋊C3 ⋊ C2 |
| Hall | C13×C73 ⋊ C3×D3 |
| Hall | C3×C73⋊C3 ⋊ D13 |
| Sylow | C73 ⋊ C3×D39 |
| Sylow | C13 ⋊ D3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C73 | C2×C3 |
| LCS | G ▷ C3×C13×C73 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2847 |
567 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D39×D73⋊C3, (C3⋊(D73⋊C3))⋊D13, D3×D13×C73⋊C3, … |
| maximal normal subgroup of | D39×D73⋊C3, (C3⋊(D73⋊C3))⋊D13, D3×D13×C73⋊C3, … |
| maximal quotient of | Dic39×C73⋊C3, C2×D39×C73⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 69);