Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C1 |
| direct product | C3×#4512 |
| Sylow | C32 ⋊ #347 |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#347, C2×C3×#4512, D3×#4512, … |
| maximal normal subgroup of | C3×D3×#347, C2×C3×#4512, D3×#4512, … |
| maximal quotient of | C3×#67511, C3×#67512, C3×#67811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1138);