Finite Group DatabasebetaFinite Group Databasebeta| order | 16614 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C13⋊C3×D71 |
| unambiguous semidirect product | C71⋊(C2×C3×C13⋊C3) |
| unambiguous semidirect product | (C13×D71)⋊C32 |
| unambiguous semidirect product | (C3×C13×D71)⋊C3 |
| Fitting, socle | C3×C13×C71 ⋊ C2×C3 |
| derived, Hall | C13×C71 ⋊ C2×C32 |
| Hall | C3×C13⋊C3×C71 ⋊ C2 |
| Hall | C13×D71 ⋊ C32 |
| Sylow | C71 ⋊ C2×C3×C13⋊C3 |
| Sylow | C13 ⋊ C32×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C13⋊C3×D71 |
| commutator, cosocle, hypocenter | C13×C71 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C71 | C2×C3 |
| LCS | G ▷ C13×C71 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2769 |
777 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13⋊C3×D71, D71×C3⋊(D13⋊C3), D3×C13⋊C3×D71, … |
| maximal normal subgroup of | C3×D13⋊C3×D71, D71×C3⋊(D13⋊C3), D3×C13⋊C3×D71, … |
| maximal quotient of | C3×C13⋊C3×Dic71, C2×C3×C13⋊C3×D71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16614, 16);