Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×A4×C3⋊C16 |
| unambiguous semidirect product | (C2×C3)⋊(A4×C16) |
| unambiguous semidirect product | (C23×C3⋊C16)⋊C3 |
| derived | C22×C3 ⋊ C2×C3×C16 |
262 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155326);