Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19128625 |
| Fitting, socle, derived | C3×C7×C127 ⋊ C2×C3 |
| Hall | C3×#14581887 ⋊ C2 |
| Hall | C7×C127 ⋊ C3×D3 |
| Sylow | C127 ⋊ D3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3⋊(D127⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C127 | C2×C3 |
| LCS | G ▷ C3×C7×C127 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,127|c^a=c^2,e^a=e^126,d^b=d^2,e^b=e^19456 conjugacy classes — view the full character table.
| maximal subgroup of | #19128629⋊D3, #19128633⋊D3, D3×#19128625, … |
| maximal normal subgroup of | #19128629⋊D3, #19128633⋊D3, D3×#19128625, … |
| maximal quotient of | C3⋊#24922580, C2×C3⋊#19128625 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 82);