Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C32×C11 ⋊ C22⋊C4 |
| Sylow | C11 ⋊ #3722 |
| Sylow | C32 ⋊ (C2×D11)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×D33 |
| commutator | C2×C32×C11 | C2×C4 |
| Fitting, socle, cosocle | C22×C32×C11 | C22 |
| prime radical | C22×C3⋊D33 | C2 |
| hypocenter | C32×C11 | C22⋊C4 |
| LCS | G ▷ C2×C32×C11 ▷ C32×C11 | |
| UCS | C1 ◁ C22 | |
168 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3^2,11|a^2=d,b^2=cd,b^a=bc,e^a=e^2,g^a=g^10,f^b=f^2210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 255);