Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#5132 |
| Fitting | C2×C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ #413 |
334 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69014, C3×#69898, #11783848, … |
| maximal normal subgroup of | C3×#69014, C3×#69898, #11783848, … |
| maximal quotient of | C3×#70782, C3×#69919, C3×#70826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4111);