Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C3×#131 ⋊ D3 |
160 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^3,3^2,2^3|b^2=c,c^2=h,f^2=h,g^2=h,b^a=bc,c^a=ch,d^a=d^2,e^a=e^2,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh48 conjugacy classes — view the full character table.
| maximal subgroup of | #11921821, D3×#5406, #11921829, … |
| maximal normal subgroup of | #11921821, D3×#5406, #11921829, … |
| maximal quotient of | #11920967, #11920972, #11920977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5522);