Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#896 |
| Fitting | C2×C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C2×C22⋊Q8 |
690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#68147, #11774115, C3×C4×#896, … |
| maximal normal subgroup of | C3×#68147, #11774115, C3×C4×#896, … |
| maximal quotient of | C2×C3×#4667, C2×C3×#4989, C2×C3×#4668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7487);