Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D3×(C2×D3)⋊C4 |
| Fitting | C22×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ C22×C22⋊C4 |
1414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4468, #11773856, D3×#4666, … |
| maximal normal subgroup of | D3×#4468, #11773856, D3×#4666, … |
| maximal quotient of | C2×D3×C3⋊#95, C4×D3×(C2×D3)⋊C4, C2×Dic3×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6935);