Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×#893 |
| Fitting | C32×C4⋊C4 ⋊ C22 |
| 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×#4872, D3×#4788, … |
| maximal normal subgroup of | D3×#4756, D3×#4872, D3×#4788, … |
| maximal quotient of | D3×#4666, D3×Dic3×C4⋊C4, #11800810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6485);