Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
172 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 25 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:
2^4,3^2,2^2|b^2=c,c^2=d,b^a=bc,c^a=cd,f^a=f^2,e^b=e^2,g^b=h,h^b=g,g^e=h,h^e=gh39 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#204, #11921802, #11921808, … |
| maximal normal subgroup of | S4×#204, #11921802, #11921808, … |
| maximal quotient of | #11920507, #11920515, #11920545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5068);