Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of C3⋊(C11⋊S4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊(C11⋊SL(2,ℤ/4)) |
| unambiguous semidirect product | C11⋊(C3⋊SL(2,ℤ/4)) |
| unambiguous semidirect product | A4⋊Dic33 |
| derived | C3×C11×A4 ⋊ C4 |
| Sylow | C11 ⋊ C3⋊SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C11⋊S4) |
| commutator, hypocenter | C3×C11×A4 | C4 |
| Fitting, socle | C23×C3×C11 | D3 |
| prime radical, cosocle | C2×C3×C11×A4 | C2 |
| LCS | G ▷ C3×C11×A4 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
Polycyclic presentation:
2^2,3^2,11,2^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,f^a=fg,f^c=g,g^c=fg138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 454);