Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C73 · Schur multiplier (H2) = C1 |
| direct product | C13×D9×C73 |
| unambiguous semidirect product | C9⋊(C2×C13×C73) |
| Fitting, Hall | C9×C13×C73 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C13×C73 |
| Hall | C9×C73 ⋊ C2×C13 |
| Hall | C9×C13 ⋊ C2×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C73 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C13×C73 |
| Frattini | C3 | D3×C13×C73 |
| Fitting | C9×C13×C73 | C2 |
| socle | C3×C13×C73 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C13×C73 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8541 |
5694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D9×D73, D9×D13×C73, D9×D949, … |
| maximal normal subgroup of | C13×D9×D73, D9×D13×C73, D9×D949, … |
| maximal quotient of | C13×Dic9×C73, C2×C13×D9×C73 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 9);