Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊(C3⋊C8) |
| derived, Hall | C32×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ D3×C3⋊C8 |
| Sylow | C32 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | (C3⋊D3)⋊D11 |
| commutator, hypocenter | C32×C11 | C2×C8 |
| Fitting, cosocle | C32×C4×C11 | C22 |
| socle | C2×C32×C11 | C2×C4 |
| prime radical | C2×C3×D33 | C4 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C4 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
Polycyclic presentation:
2^4,3^2,11|b^2=c,c^2=d,e^a=e^2,g^a=g^10,e^b=e^2,f^b=f^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 259);