Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C127⋊C7 |
| unambiguous semidirect product | C3⋊(C2×C3×C127⋊C7) |
| unambiguous semidirect product | (C3×D3×C127)⋊C7 |
| Fitting, socle, Hall | C32×C127 ⋊ C2×C7 |
| derived | C3×C127 ⋊ C2×C3×C7 |
| Hall | C32×C127⋊C7 ⋊ C2 |
| Hall | C3×D3×C127 ⋊ C7 |
| Sylow | C127 ⋊ C3×D3×C7 |
| Sylow | C32 ⋊ C2×C127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C127⋊C7 |
| commutator, cosocle, hypocenter | C3×C127 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C127 | C2×C7 |
| LCS | G ▷ C3×C127 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×D127⋊C7, D3×C3⋊(D127⋊C7), D32×C127⋊C7, … |
| maximal normal subgroup of | C3×D3×D127⋊C7, D3×C3⋊(D127⋊C7), D32×C127⋊C7, … |
| maximal quotient of | C3×Dic3×C127⋊C7, C2×C3×D3×C127⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 52);