Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C3⋊D3×#385 |
| Fitting | C32×#385 ⋊ C2 |
| Sylow | C32 ⋊ C2×#385 |
3696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C3⋊D3×#120, C3⋊D3×#65699, #72260305 |
| maximal normal subgroup of | C4×C3⋊D3×#120, #72260305 |
| maximal quotient of | C3⋊D3×#65699 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 35254);