Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×D127⋊C7 |
| unambiguous semidirect product | (C32×D127)⋊C7 |
| Fitting, socle, Hall | C32×C127 ⋊ C2×C7 |
| derived, Sylow | C127 ⋊ C2×C32×C7 |
| Hall | C32×C127⋊C7 ⋊ C2 |
| Hall | C32×D127 ⋊ C7 |
| Hall | C127⋊C7 ⋊ C2×C32 |
| Hall | D127 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D127⋊C7 |
| commutator, cosocle, hypocenter | C127 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C127 | C2×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
207 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×D127⋊C7, C3⋊D3×D127⋊C7, C2×C32×D127⋊C7 |
| maximal normal subgroup of | C3×D3×D127⋊C7, C3⋊D3×D127⋊C7, C2×C32×D127⋊C7 |
| maximal quotient of | C32×Dic127⋊C7, C2×C32×D127⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 50);