Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C42 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×A4×#97 |
| unambiguous semidirect product | (C22×#97)⋊C32 |
| unambiguous semidirect product | (C22×C3×#97)⋊C3 |
| Fitting | C22×C3×#97 ⋊ C3 |
| Sylow | C22×#97 ⋊ C32 |
440 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | A42×#97, #97×C3⋊S4 |
| maximal normal subgroup of | #97×C3⋊S4 |
| maximal quotient of | A42×#97 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153529);