Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#5128 |
| Fitting | C2×C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ #436 |
278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#436, C2×C3×#5128, D3×#5128, … |
| maximal normal subgroup of | C3×D3×#436, C2×C3×#5128, D3×#5128, … |
| maximal quotient of | C3×#70859, C3×#70866, C3×#70950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4107);