Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3 |
| direct product | C3⋊D3×#518 |
| Fitting | C32×#518 ⋊ C2 |
| Sylow | C32 ⋊ C2×#518 |
5760 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3484, C3⋊D3×#1889, #72214673, … |
| maximal normal subgroup of | C3⋊D3×#3484, C3⋊D3×#1889, #72214673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134003);