Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#4493 |
| Sylow | C32 ⋊ #368 |
95 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#368, C2×C3×#4493, D3×#4493, … |
| maximal normal subgroup of | C3×D3×#368, C2×C3×#4493, D3×#4493, … |
| maximal quotient of | C3×#67469, C3×#67470, C3×#67728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1119);