Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#909 |
| Fitting | C2×C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ C2×#137 |
550 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69004, C3×#68775, #11787699, … |
| maximal normal subgroup of | C3×#69004, C3×#68775, #11787699, … |
| maximal quotient of | C2×C3×#5120, C2×C3×#5133, C2×C3×#5121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7726);