Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(D127⋊C7)) |
| unambiguous semidirect product | (C127⋊C7)⋊(C3⋊D3) |
| unambiguous semidirect product | (C3⋊D381)⋊C7 |
| Fitting, socle, derived, Hall | C32×C127 ⋊ C2×C7 |
| Hall | C32×C127⋊C7 ⋊ C2 |
| Hall | C3⋊D381 ⋊ C7 |
| Hall | C127⋊C7 ⋊ C3⋊D3 |
| Sylow | C127 ⋊ C7×C3⋊D3 |
| Sylow | C32 ⋊ D127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C127 | C2×C7 |
| LCS | G ▷ C32×C127 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,3^2,127|c^a=c^2,d^a=d^2,e^a=e^126,e^b=e^4123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 53);