Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of C11⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C11⋊#3708 |
| derived, Hall | C32×C11 ⋊ C16 |
| Sylow | C11 ⋊ #3708 |
| Sylow | C32 ⋊ C11⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C11⋊#157 |
| commutator, hypocenter | C32×C11 | C16 |
| Fitting | C32×C4×C11 | C4 |
| socle, prime radical | C2×C32×C11 | C8 |
| cosocle | C11×C3⋊(C3⋊C8) | C2 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C4 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
Polycyclic presentation:
2^4,3^2,11|a^2=b,b^2=c,c^2=d,e^a=ef,f^a=ef^2,g^a=g^10,e^b=e^2,f^b=f^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 167);