Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×C3×#938 |
| Fitting | C22×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ C2×#121 |
970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70200, #11787323, C3×#70201, … |
| maximal normal subgroup of | C3×#70200, #11787323, C3×#70201, … |
| maximal quotient of | C2×C3×#4987, C2×C3×#4956, C2×C3×#4944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7779);