Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D32⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C32×C11 ⋊ C4⋊C4 |
| Sylow | C11 ⋊ #3773 |
| Sylow | C32 ⋊ Dic11⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32⋊D11 |
| commutator | C11×C3⋊D3 | C2×C4 |
| Fitting, socle | C2×C32×C11 | D4 |
| prime radical, cosocle | C2×C11×C3⋊D3 | C22 |
| hypocenter | C32×C11 | C4⋊C4 |
| LCS | G ▷ C11×C3⋊D3 ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3^2,11|a^2=d,b^2=d,b^a=bc,e^a=e^2,f^a=e^2f,g^a=g^10,e^b=e^2f^2,e^c=e^2,f^c=f^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 391);