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 ⋊ (C2×D3)⋊Dic3 |
| Sylow | C32 ⋊ (C2×D11)⋊C4 |
152 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 528 |
Polycyclic presentation:
2^4,3^2,11|b^2=c,b^a=bd,e^a=e^2,g^a=g^10,e^b=e^2,f^b=f^2150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 271);