Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#4989 |
| Fitting | C2×C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #385 |
514 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#385, C2×C3×#4989, D3×#4989, … |
| maximal normal subgroup of | C3×D3×#385, C2×C3×#4989, D3×#4989, … |
| maximal quotient of | C3×(C2×D3)⋊#95, C3×#69406, C3×#71564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3968);