Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #358 |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=df,b^2=cde,c^2=ef,e^2=f,g^3=h^2,b^a=bc,c^a=ce,e^a=ef,g^a=g^2h,h^a=h^2150 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#358, C2×#10588180, #11796633, … |
| maximal normal subgroup of | D9×#358, C2×#10588180, #11796633, … |
| maximal quotient of | #11771587, #11771870, #11772080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 62);