Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×#11765917 |
| derived, Sylow | C127 ⋊ C2×C7×C9 |
| Hall | C2×C7×C127 ⋊ C9 |
| Hall | C7×C127 ⋊ C2×C9 |
| Hall | C2×C127 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | C127⋊C3 |
| commutator, hypocenter | C127 | C2×C7×C9 |
| Frattini | C3 | C2×C7×C127⋊C3 |
| Fitting, socle, prime radical | C2×C3×C7×C127 | C3 |
| cosocle | C3×C127 | C2×C3×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C3×C7 | |
24 conjugacy classes of subgroups.
1890 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C7×#11765917, C7×#11765917⋊C4, Dic7×#11765917, … |
| maximal normal subgroup of | C4×C7×#11765917, C7×#11765917⋊C4, Dic7×#11765917, … |
| maximal quotient of | C4×C7×#11765917, C22×C7×#11765917 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 3);