Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#5822 |
| Fitting | C2×C32×#41 ⋊ C2 |
| Sylow | C32 ⋊ #575 |
606 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70416, C3×#70293, C3×#72020, … |
| maximal normal subgroup of | C3×#70416, C3×#70293, C3×#72020, … |
| maximal quotient of | C3×#82213, C3×#84072, C3×#82207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7801);