Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #468 |
265 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 265 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|b^2=f,c^2=def,e^2=f,b^a=bd,c^a=cf,h^a=h^2,c^b=ce,e^b=ef,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5134, C2×#10590850, #11866937, … |
| maximal normal subgroup of | D3×#5134, C2×#10590850, #11866937, … |
| maximal quotient of | #11781636, #11781682, #11781859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2732);