Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×A4×AGL(1,ℤ/8) |
| unambiguous semidirect product | (C22×AGL(1,ℤ/8))⋊C32 |
| unambiguous semidirect product | (C22×C3×AGL(1,ℤ/8))⋊C3 |
| Fitting | C22×C3×AGL(1,ℤ/8) ⋊ C3 |
| Sylow | C22×AGL(1,ℤ/8) ⋊ C32 |
936 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | A42×AGL(1,ℤ/8), AGL(1,ℤ/8)×C3⋊S4, C3×S4×AGL(1,ℤ/8), … |
| maximal normal subgroup of | AGL(1,ℤ/8)×C3⋊S4, C3×S4×AGL(1,ℤ/8), D3×A4×AGL(1,ℤ/8) |
| maximal quotient of | A42×AGL(1,ℤ/8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153805);