Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C4×D3×A4 |
| unambiguous semidirect product | (C23×C4×D3)⋊C3 |
| Fitting | C23×C3×C4 ⋊ C2×C3 |
| derived | C22×C3 ⋊ C22×C3×C4 |
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D3)⋊(A4⋊C8), A4×(C2×D3)⋊C8, C2×D3×A4⋊C8, … |
| maximal normal subgroup of | (C2×D3)⋊(A4⋊C8), A4×(C2×D3)⋊C8, C2×D3×A4⋊C8, … |
| maximal quotient of | C4×A4×Dic6, C42×D3×A4, A4×#872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8490);