Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×M32 |
| unambiguous semidirect product | (C22×M32)⋊C32 |
| unambiguous semidirect product | (C22×C3×M32)⋊C3 |
| Fitting | C22×C3×M32 ⋊ C3 |
| Sylow | C22×M32 ⋊ C32 |
272 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | A42×M32 |
| maximal quotient of | A42×M32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153629);