Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C9⋊C16) |
| Sylow | C9 ⋊ C4⋊C16 |
75 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=e,e^2=f,g^3=h^2,b^a=bd,g^a=g^2h,h^a=h^2168 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊(C9⋊C16), #11771531, #11771547, … |
| maximal normal subgroup of | D4⋊(C9⋊C16), #11771531, #11771547, … |
| maximal quotient of | #11772163, #11772206, #11772260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 21);