Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D9×C127⋊C7 |
| unambiguous semidirect product | C9⋊(C2×C127⋊C7) |
| unambiguous semidirect product | (D9×C127)⋊C7 |
| Fitting, derived, Hall | C9×C127 ⋊ C2×C7 |
| Hall | C9×C127⋊C7 ⋊ C2 |
| Hall | D9×C127 ⋊ C7 |
| Sylow | C127 ⋊ C7×D9 |
| Sylow | C9 ⋊ C2×C127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C127 | C2×C7 |
| Frattini | C3 | D3×C127⋊C7 |
| socle | C3×C127 | D3×C7 |
| LCS | G ▷ C9×C127 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
150 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D127⋊C7, C2×D9×C127⋊C7 |
| maximal normal subgroup of | D9×D127⋊C7, C2×D9×C127⋊C7 |
| maximal quotient of | Dic9×C127⋊C7, C2×D9×C127⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 16);