Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #452 |
329 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,h^a=h^2,c^b=ce,d^b=df,g^b=g^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5047, D3×#5239, #11863779, … |
| maximal normal subgroup of | D3×#5047, D3×#5239, #11863779, … |
| maximal quotient of | #11778296, #11778409, #11778748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3052);