Finite Group DatabasebetaFinite Group Databasebeta| order | 16218 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C53 · Schur multiplier (H2) = C3 |
| direct product | C17×C3⋊D3×C53 |
| unambiguous semidirect product | C3⋊(D3×C17×C53) |
| Fitting, socle, Hall | C32×C17×C53 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C17×C53 |
| Hall | C32×C53 ⋊ C2×C17 |
| Hall | C32×C17 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C53 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C17×C53 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C53 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C17×C53 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8109 |
5406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×#157×C53, C17×#14274232, C53×#10597480, … |
| maximal normal subgroup of | C17×#157×C53, C17×#14274232, C53×#10597480, … |
| maximal quotient of | C17×C3⋊Dic3×C53, C2×C17×C3⋊D3×C53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16218, 13);