Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×C3⋊#564 |
| unambiguous semidirect product | C3⋊(C3×#564) |
| Sylow | C32 ⋊ #564 |
372 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71250, C3×#68375, #11780550, … |
| maximal normal subgroup of | C3×#71250, C3×#68375, #11780550, … |
| maximal quotient of | C3×#75993, C3×#74978, C3×#74979, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7665);