Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C32 ⋊ #575 |
786 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|e^2=f,d^a=df,g^a=g^2,h^a=h^2,c^b=cf,d^c=de,e^c=ef,e^d=ef66 conjugacy classes — view the full character table.
| maximal subgroup of | #11787631, #11788574, #11861096, … |
| maximal normal subgroup of | #11787631, #11788574, #11861096, … |
| maximal quotient of | #11857933, #11857939, #11858495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8126);