Finite Group DatabasebetaFinite Group Databasebeta| order | 16764 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊((C127⋊C3)⋊C4) |
| unambiguous semidirect product | (C127⋊C3)⋊Dic11 |
| unambiguous semidirect product | Dic1397⋊C3 |
| derived, Hall | C11×C127 ⋊ C3×C4 |
| Hall | Dic1397 ⋊ C3 |
| Hall | C11×C127⋊C3 ⋊ C4 |
| Hall | C127⋊C3 ⋊ Dic11 |
| Sylow | C127 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ (C127⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(D127⋊C3) |
| commutator, hypocenter | C11×C127 | C3×C4 |
| Fitting, socle, cosocle | C2×C11×C127 | C2×C3 |
| prime radical | C2×C11×C127⋊C3 | C2 |
| LCS | G ▷ C11×C127 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5588 |
Polycyclic presentation:
2,3,11,127,2|a^2=e,c^a=c^10,d^a=d^126,d^b=d^107504 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16764, 12);