Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#4511 |
| Sylow | C32 ⋊ #364 |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#364, C2×C3×#4511, D3×#4511, … |
| maximal normal subgroup of | C3×D3×#364, C2×C3×#4511, D3×#4511, … |
| maximal quotient of | C3×#67554, C3×#67555, C3×#67810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1137);