Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5706 |
| Fitting | C32×#126 ⋊ C2 |
| Sylow | C32 ⋊ #529 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#529, C2×C3×#5706, D3×#5706, … |
| maximal normal subgroup of | C3×D3×#529, C2×C3×#5706, D3×#5706, … |
| maximal quotient of | C3×#74258, C3×#74937, C3×#75449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7685);