Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×Dic3×M16 |
| Sylow | C32 ⋊ C4×M16 |
318 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#68972, C3×Dic3×#100, Dic3×#823, … |
| maximal normal subgroup of | C3×#68972, C3×Dic3×#100, Dic3×#823, … |
| maximal quotient of | C3×M16×C3⋊C8, C3×#70739, C3×#69847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4096);