Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C127⋊C7 |
| unambiguous semidirect product | C3⋊(D3×C127⋊C7) |
| unambiguous semidirect product | (C3⋊D3×C127)⋊C7 |
| Fitting, socle, derived, Hall | C32×C127 ⋊ C2×C7 |
| Hall | C32×C127⋊C7 ⋊ C2 |
| Hall | C3⋊D3×C127 ⋊ C7 |
| Sylow | C127 ⋊ C7×C3⋊D3 |
| Sylow | C32 ⋊ C2×C127⋊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.
150 conjugacy classes — view the full character table.
| maximal subgroup of | (C127⋊C7)⋊#157, #157×C127⋊C7, (C3⋊D3)⋊(D127⋊C7), … |
| maximal normal subgroup of | (C127⋊C7)⋊#157, #157×C127⋊C7, (C3⋊D3)⋊(D127⋊C7), … |
| maximal quotient of | C3⋊Dic3×C127⋊C7, C2×C3⋊D3×C127⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 54);