Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×D3×#322 |
| Fitting | C32×#322 ⋊ C2 |
| Sylow | C32 ⋊ C2×#322 |
529 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#1715, C3×D3×#1721, C3×D3×#1455, … |
| maximal normal subgroup of | C3×D3×#1715, C3×D3×#1721, C3×D3×#1455 |
| maximal quotient of | AGL(1,ℤ/9)×#322 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7515);