Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#4463 |
| Sylow | C32 ⋊ #364 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67766, C3×#67441, #11771647, … |
| maximal normal subgroup of | C3×#67766, C3×#67441, #11771647, … |
| maximal quotient of | C3×#67439, C3×#67440, C3×#67658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1089);