Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽127) |
| unambiguous semidirect product | (#11765919⋊C2)⋊C7 |
| unambiguous semidirect product | (#11765919⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C127 ⋊ C2×C7×C9 |
| Hall | #11765919⋊C7 ⋊ C2 |
| Hall | #11765919⋊C2 ⋊ C7 |
| Hall | D127⋊C7 ⋊ C9 |
| Hall | #11765919 ⋊ C2×C7 |
| Hall | C127⋊C7 ⋊ C2×C9 |
| Hall | D127 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C127 | C2×C7×C9 |
| prime radical | (D127⋊C3)⋊C7 | C3 |
| cosocle | C127⋊C3 | C2×C3×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,3,127|b^3=d,e^a=e^126,e^b=e^68,e^c=e^4,e^d=e^107127 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽127) |
| maximal normal subgroup of | C2×AGL(1,𝔽127) |
| maximal quotient of | (#11765919⋊C4)⋊C7, C2×AGL(1,𝔽127) |
| automorphism group of | D127 |
| holomorph of | C127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 32);