Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C8 · Schur multiplier (H2) = C24×C3 |
| direct product | C22×C3×C8×A4 |
| Fitting | C24×C3×C8 ⋊ C3 |
| derived | C22 ⋊ C22×C32×C8 |
| Sylow | C24×C8 ⋊ C32 |
1064 conjugacy classes of subgroups; only the 304 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 304 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153785);