Finite Group DatabasebetaFinite Group Databasebeta| order | 16302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D209 |
| unambiguous semidirect product | C11⋊(D19×C13⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C19 | C2×C3 |
| LCS | G ▷ C11×C13×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2717 |
742 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13⋊C3×D209, (C11⋊(D13⋊C3))⋊D19, D11×D19×C13⋊C3, … |
| maximal normal subgroup of | D13⋊C3×D209, (C11⋊(D13⋊C3))⋊D19, D11×D19×C13⋊C3, … |
| maximal quotient of | C13⋊C3×Dic209, C2×C13⋊C3×D209 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16302, 38);