Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D381 |
| unambiguous semidirect product | C3⋊(C3×C7×D127) |
| Fitting, socle, Hall | C32×C7×C127 ⋊ C2 |
| derived | C3×C127 ⋊ C2×C3×C7 |
| Hall | C32×C127 ⋊ C2×C7 |
| Hall | C7×C127 ⋊ C3×D3 |
| Sylow | C127 ⋊ C3×D3×C7 |
| Hall | C32×C7 ⋊ D127 |
| Sylow | C32 ⋊ C7×D127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D381 |
| commutator, cosocle, hypocenter | C3×C127 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C127 | C2 |
| LCS | G ▷ C3×C127 | |
| UCS | C1 ◁ C3×C7 | |
36 conjugacy classes of subgroups.
4032 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C7×D127, C3×D7×D381, C3×D21⋊D127, … |
| maximal normal subgroup of | C3×D3×C7×D127, C3×D7×D381, C3×D21⋊D127, … |
| maximal quotient of | C3×C7×Dic381, C2×C3×C7×D381 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 98);