Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1143 |
| unambiguous semidirect product | C9⋊(C7×D127) |
| Fitting, Hall | C7×C9×C127 ⋊ C2 |
| derived, Hall | C9×C127 ⋊ C2×C7 |
| Hall | C7×C127 ⋊ D9 |
| Sylow | C127 ⋊ C7×D9 |
| Hall | C7×C9 ⋊ D127 |
| Sylow | C9 ⋊ C7×D127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1143 |
| commutator, cosocle, hypocenter | C9×C127 | C2×C7 |
| Frattini | C3 | C7×D381 |
| Fitting | C7×C9×C127 | C2 |
| socle | C3×C7×C127 | D3 |
| LCS | G ▷ C9×C127 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
4011 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D9×D127, D7×D1143, D63⋊D127, … |
| maximal normal subgroup of | C7×D9×D127, D7×D1143, D63⋊D127, … |
| maximal quotient of | C7×Dic1143, C2×C7×D1143 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 12);