Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C32×C11 ⋊ M16 |
| Sylow | C11 ⋊ #3743 |
| Sylow | C32 ⋊ #4318 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C3⋊D3×D11 |
| commutator, socle | C2×C32×C11 | C2×C4 |
| Fitting, cosocle | C32×C4×C11 | C22 |
| prime radical | C2×C11×C3⋊D3 | C4 |
| hypocenter | C32×C11 | M16 |
| LCS | G ▷ C2×C32×C11 ▷ C32×C11 | |
| UCS | C1 ◁ C4 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
Polycyclic presentation:
2^4,3^2,11|a^2=c,c^2=d,b^a=bd,g^a=g^10,e^b=e^2,f^b=f^2162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 197);