Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×GL(2,ℤ/4)⋊C4 |
| unambiguous semidirect product | GL(2,ℤ/4)⋊(C3×C4) |
| Fitting | C22×C3×C22⋊C4 ⋊ D3 |
948 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11923458, D3×GL(2,ℤ/4)⋊C4, C3×#11714540, … |
| maximal normal subgroup of | D3×GL(2,ℤ/4)⋊C4, C3×#11714540, #72253012 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156592);