Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((D127⋊C3)⋊C7) |
| unambiguous semidirect product | (C3⋊(D127⋊C3))⋊C7 |
| unambiguous semidirect product | ((C127⋊C3)⋊C7)⋊D3 |
| unambiguous semidirect product | (C3⋊(D127⋊C7))⋊C3 |
| Fitting, socle, derived | C3×C127 ⋊ C2×C3×C7 |
| Hall | C3×(C127⋊C3)⋊C7 ⋊ C2 |
| Hall | C3⋊(D127⋊C3) ⋊ C7 |
| Hall | C3×C127⋊C3 ⋊ C2×C7 |
| Hall | C127⋊C7 ⋊ C3×D3 |
| Sylow | C127 ⋊ C3×D3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C127 | C2×C3×C7 |
| LCS | G ▷ C3×C127 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,3,127|d^a=d^2,e^a=e^126,e^b=e^107,e^c=e^472 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, 35);