Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#4519 |
| Fitting | C32×D16 ⋊ C2 |
| Sylow | C32 ⋊ D32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×D32, C2×C3×#4519, D3×#4519, … |
| maximal normal subgroup of | C3×D3×D32, C2×C3×#4519, D3×#4519, … |
| maximal quotient of | C3×#67577, C3×#67824, C3×#67575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1145);