Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×A4×#137 |
| unambiguous semidirect product | (C22×#137)⋊C32 |
| unambiguous semidirect product | (C22×C3×#137)⋊C3 |
| Fitting | C22×C3×#137 ⋊ C3 |
| Sylow | C22×#137 ⋊ C32 |
808 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153807);