Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | A4×#914 |
| unambiguous semidirect product | (C22×#914)⋊C3 |
| Fitting | C22×C3×SD16 ⋊ C2×C3 |
820 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72274463, S4×#914, D3×A4×AGL(1,ℤ/8) |
| maximal normal subgroup of | #72274463, S4×#914, D3×A4×AGL(1,ℤ/8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157335);