Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×A4×C22⋊Q8 |
| unambiguous semidirect product | (C22×C22⋊Q8)⋊C32 |
| unambiguous semidirect product | (C22×C3×C22⋊Q8)⋊C3 |
| Fitting | C22×C3×C22⋊Q8 ⋊ C3 |
| Sylow | C22×C22⋊Q8 ⋊ C32 |
1008 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153707);