Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5664 |
| Fitting | C32×#123 ⋊ C2 |
| Sylow | C32 ⋊ #559 |
511 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71002, C3×#69140, #11798609, … |
| maximal normal subgroup of | C3×#71002, C3×#69140, #11798609, … |
| maximal quotient of | C3×#74963, C3×#74061, C3×#75476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7643);