Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C3×C4×D3×M16 |
| Fitting | C32×C4×M16 ⋊ C2 |
| Sylow | C32 ⋊ C2×C4×M16 |
1383 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D32×M16, C3×D3×#3151, D3×#78530, … |
| maximal normal subgroup of | C4×D32×M16, C3×D3×#3151, D3×#78530, … |
| maximal quotient of | C4×M16×AGL(1,ℤ/9), C3×D3×#1455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91146);