Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#568⋊C3 |
| unambiguous semidirect product | (D3×#568)⋊C3 |
| Fitting | C3×#568 ⋊ C2×C3 |
708 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3585⋊C3, D3×#85453, D3×#85454 |
| maximal normal subgroup of | D3×#3585⋊C3, D3×#85453, D3×#85454 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157327);