Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #485 |
230 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 64 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|a^2=ef,b^2=d,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^2,c^b=cef,g^b=g^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5045, D3×#4723, #11869502, … |
| maximal normal subgroup of | D3×#5045, D3×#4723, #11869502, … |
| maximal quotient of | #11785822, #11786510, #11787288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3009);