Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #339 |
165 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=f,e^2=f,g^3=h^2,b^a=be,e^a=ef,g^a=g^2h,h^a=h^2,e^b=ef108 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#339, C2×#10588208, #11783195, … |
| maximal normal subgroup of | D9×#339, C2×#10588208, #11783195, … |
| maximal quotient of | #11770732, #11770761, #11770787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 90);