Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#4727 |
| Fitting | C32×C22⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ #408 |
341 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#408, C2×C3×#4727, D3×#4727, … |
| maximal normal subgroup of | C3×D3×#408, C2×C3×#4727, D3×#4727, … |
| maximal quotient of | C3×#68122, C3×#68146, C3×#68104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3706);