Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C127 ⋊ C2×C3×C7 |
| derived, Sylow | C127 ⋊ C2×C32×C7 |
| Hall | C3×(C127⋊C3)⋊C7 ⋊ C2 |
| Hall | C3×D127⋊C3 ⋊ C7 |
| Hall | D127⋊C7 ⋊ C32 |
| Hall | C3×C127⋊C3 ⋊ C2×C7 |
| Hall | C127⋊C7 ⋊ C2×C32 |
| Hall | D127 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (D127⋊C3)⋊C7 |
| commutator, cosocle, hypocenter | C127 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C127 | C2×C3×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
135 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(D127⋊C3)⋊C7, C2×C3×(D127⋊C3)⋊C7 |
| maximal normal subgroup of | D3×(D127⋊C3)⋊C7, C2×C3×(D127⋊C3)⋊C7 |
| maximal quotient of | C3×((C127⋊C3)⋊C4)⋊C7, C2×C3×(D127⋊C3)⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 34);