Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊D127 |
| derived, Hall | C7×C127 ⋊ C2×C9 |
| Hall | C7⋊C9×C127 ⋊ C2 |
| Hall | D889 ⋊ C9 |
| Sylow | C127 ⋊ D7⋊C9 |
| Hall | C7⋊C9 ⋊ D127 |
| Sylow | C7 ⋊ C9×D127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊D127 |
| commutator, hypocenter | C7×C127 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C127 | C2×C3 |
| prime radical | C3×D889 | C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,127,3|b^3=e,c^a=c^6,d^a=d^126,c^b=c^2966 conjugacy classes — view the full character table.
| maximal subgroup of | D7⋊C9×D127, C2×(C7⋊C9)⋊D127 |
| maximal normal subgroup of | D7⋊C9×D127, C2×(C7⋊C9)⋊D127 |
| maximal quotient of | (C7⋊C9)⋊Dic127, C2×(C7⋊C9)⋊D127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 27);