Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5662 |
| Fitting | C32×#123 ⋊ C2 |
| Sylow | C32 ⋊ #542 |
471 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#542, C2×C3×#5662, D3×#5662, … |
| maximal normal subgroup of | C3×D3×#542, C2×C3×#5662, D3×#5662, … |
| maximal quotient of | C3×#75456, C3×#74055, C3×#74946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7641);