Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×#100 ⋊ C2 |
| Sylow | C32 ⋊ AΣL(1,𝔽16) |
282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^2|b^2=c,c^2=f,b^a=bd,c^a=ce,g^a=g^2,h^a=h^2,d^b=de,e^b=ef,d^c=df57 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×AΣL(1,𝔽16), C2×#10589341, D3×#4475, … |
| maximal normal subgroup of | C3⋊D3×AΣL(1,𝔽16), C2×#10589341, D3×#4475, … |
| maximal quotient of | #11771361, #11771490, #11771786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1223);