Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C4 |
| direct product | C3×#83937 |
| Fitting | C2×C32×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C32 ⋊ #3151 |
1461 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#3151, #72244777, D3×#83937, … |
| maximal normal subgroup of | C3×D3×#3151, D3×#83937, #72252603 |
| maximal quotient of | #72244777, C3×#10784430, C3×#10784426 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108470);