Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊(C9⋊C8) |
| Sylow | C9 ⋊ D4⋊C8 |
123 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=c,c^2=e,d^2=f,g^3=h^2,b^a=bd,d^a=df,g^a=g^2h,h^a=h^2,d^b=df108 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D4⋊C8, C2×D4⋊(C9⋊C8), #11774222, … |
| maximal normal subgroup of | D9×D4⋊C8, C2×D4⋊(C9⋊C8), #11774222, … |
| maximal quotient of | #11770654, #11770667, #11770787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 93);