Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×A4×D8 |
| unambiguous semidirect product | (C22×D8)⋊C32 |
| unambiguous semidirect product | (C22×C3×D8)⋊C3 |
| Fitting | C22×C3×D8 ⋊ C3 |
| Sylow | C22×D8 ⋊ C32 |
230 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4×D16, C3×A4×SD32, C2×C3×A4×D8, … |
| maximal normal subgroup of | C3×A4×D16, C3×A4×SD32, C2×C3×A4×D8, … |
| maximal quotient of | C3×A4×#102, C3×A4×#107, C3×#3358⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7434);