Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#4733 |
| Fitting | C32×C22⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ #452 |
329 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#452, C2×C3×#4733, D3×#4733, … |
| maximal normal subgroup of | C3×D3×#452, C2×C3×#4733, D3×#4733, … |
| maximal quotient of | C3×#68132, C3×#68109, C3×#68136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3712);