Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C3×C4 |
| direct product | C4×M16×C3⋊D3 |
| Fitting | C32×C4×M16 ⋊ C2 |
| Sylow | C32 ⋊ C2×C4×M16 |
1968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3151, C3⋊D3×#1455, #72214070, … |
| maximal normal subgroup of | C3⋊D3×#3151, C3⋊D3×#1455, #72214070, … |
| maximal quotient of | C3⋊D3×#1455, C4×C3⋊D3×#97 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91145);