Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×A4×M16 |
| unambiguous semidirect product | (C22×D3×M16)⋊C3 |
| Fitting | C22×C3×M16 ⋊ C2×C3 |
820 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×M16×S4, D3×A4×AGL(1,ℤ/8), D3×#85443 |
| maximal normal subgroup of | D3×M16×S4, D3×A4×AGL(1,ℤ/8), D3×#85443 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157316);