Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (#11765917⋊C2)⋊C7 |
| unambiguous semidirect product | (#11765917⋊C7)⋊C2 |
| derived, Sylow | C127 ⋊ C2×C7×C9 |
| Hall | #11765917⋊C7 ⋊ C2 |
| Hall | #11765917⋊C2 ⋊ C7 |
| Hall | D127⋊C7 ⋊ C9 |
| Hall | #11765917 ⋊ C2×C7 |
| Hall | C127⋊C7 ⋊ C2×C9 |
| Hall | D127 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (D127⋊C3)⋊C7 |
| commutator, hypocenter | C127 | C2×C7×C9 |
| Fitting, socle, cosocle | C3×C127 | C2×C3×C7 |
| prime radical | C3×D127⋊C7 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,127,3|b^3=e,d^a=d^126,d^b=d^107,d^c=d^4135 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(#11765917⋊C2)⋊C7 |
| maximal normal subgroup of | C2×(#11765917⋊C2)⋊C7 |
| maximal quotient of | (#11765917⋊C4)⋊C7, C2×(#11765917⋊C2)⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 30);