Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D21×C127⋊C3 |
| unambiguous semidirect product | C3⋊(D7×C127⋊C3) |
| Fitting, socle, derived | C3×C7×C127 ⋊ C2×C3 |
| Hall | C3×C7×C127⋊C3 ⋊ C2 |
| Hall | C3×C127⋊C3 ⋊ D7 |
| Hall | C7×C127 ⋊ C3×D3 |
| Sylow | C127 ⋊ C3×D21 |
| Sylow | C7 ⋊ D3×C127⋊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.
540 conjugacy classes — view the full character table.
| maximal subgroup of | D21×D127⋊C3, (C3⋊(D127⋊C3))⋊D7, D3×D7×C127⋊C3, … |
| maximal normal subgroup of | D21×D127⋊C3, (C3⋊(D127⋊C3))⋊D7, D3×D7×C127⋊C3, … |
| maximal quotient of | Dic21×C127⋊C3, C2×D21×C127⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 87);