Finite Group DatabasebetaFinite Group Databasebeta| order | 16764 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D127 |
| unambiguous semidirect product | D381⋊D11 |
| unambiguous semidirect product | D1397⋊D3 |
| Fitting, socle, derived, Hall | C3×C11×C127 ⋊ C22 |
| Hall | C11×C127 ⋊ C2×D3 |
| Hall | C3×C127 ⋊ C2×D11 |
| Sylow | C127 ⋊ D3×D11 |
| Hall | C3×C11 ⋊ C2×D127 |
| Sylow | C11 ⋊ D3×D127 |
| Sylow | C3 ⋊ D11×D127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C127 | C22 |
| LCS | G ▷ C3×C11×C127 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4191 |
Polycyclic presentation:
2^2,3,11,127|d^a=d^10,e^a=e^126,c^b=c^2,d^b=d^101155 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16764, 24);