Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×D4×Dic3 |
| Sylow | C32 ⋊ C2×C4×D4 |
899 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4756, D3×Dic3×D8, D3×Dic3×SD16, … |
| maximal normal subgroup of | D3×#4756, D3×Dic3×D8, D3×Dic3×SD16, … |
| maximal quotient of | D3×Dic3×C22⋊C4, D3×Dic3×C4⋊C4, Dic3×#893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7010);