Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D7×#11765917 |
| derived, Hall | C7×C127 ⋊ C2×C9 |
| Hall | C7×#11765917 ⋊ C2 |
| Hall | D7×C127 ⋊ C9 |
| Sylow | C127 ⋊ C9×D7 |
| Sylow | C7 ⋊ C2×#11765917 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D7×C127⋊C3 |
| commutator, hypocenter | C7×C127 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C127 | C2×C3 |
| prime radical | C3×D7×C127 | C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
675 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#11765917⋊C2, C2×D7×#11765917 |
| maximal normal subgroup of | D7×#11765917⋊C2, C2×D7×#11765917 |
| maximal quotient of | Dic7×#11765917, C2×D7×#11765917 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 22);