Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | A4×#67⋊C4 |
| unambiguous semidirect product | #67⋊(C4×A4) |
| unambiguous semidirect product | (C22×#67⋊C4)⋊C3 |
| Fitting | C22×C3×C22⋊C4 ⋊ C2×C3 |
1190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157166);