Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D9)⋊C16 |
| Fitting | C2×C9×C16 ⋊ C2 |
| Sylow | C9 ⋊ C22⋊C16 |
99 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=c,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 | D9×C22⋊C16, C2×(C2×D9)⋊C16, #11795970, … |
| maximal normal subgroup of | D9×C22⋊C16, C2×(C2×D9)⋊C16, #11795970, … |
| maximal quotient of | #11771334, #11771434, #11771525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 66);