Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×D3×D4×A4 |
| unambiguous semidirect product | (C23×D3×D4)⋊C3 |
| Fitting | C23×C3×D4 ⋊ C2×C3 |
4358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×A4×S4, D32×D4×A4, D3×A4×#120, … |
| maximal normal subgroup of | D3×A4×#120, D3×#85495, C2×D3×D4×S4, … |
| maximal quotient of | D32×D4×A4, D3×#3585⋊C3, D3×A4×#120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157805);