Finite Group DatabasebetaFinite Group Databasebeta| order | 16218 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C53 · Schur multiplier (H2) = C1 |
| direct product | C17×D9×C53 |
| unambiguous semidirect product | C9⋊(C2×C17×C53) |
| Fitting, Hall | C9×C17×C53 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C17×C53 |
| Hall | C9×C53 ⋊ C2×C17 |
| Hall | C9×C17 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C53 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C17×C53 |
| Frattini | C3 | D3×C17×C53 |
| Fitting | C9×C17×C53 | C2 |
| socle | C3×C17×C53 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C17×C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8109 |
5406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D9×D53, D9×D17×C53, D9×D901, … |
| maximal normal subgroup of | C17×D9×D53, D9×D17×C53, D9×D901, … |
| maximal quotient of | C17×Dic9×C53, C2×C17×D9×C53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16218, 5);