Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C42 · Schur multiplier (H2) = C23×C3×C4 |
| direct product | C2×C3×C42×A4 |
| Fitting | C23×C3×C42 ⋊ C3 |
| derived | C22 ⋊ C2×C32×C42 |
| Sylow | C23×C42 ⋊ C32 |
1576 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1576 conjugacy classes of subgroups — too many to draw. Only its 432 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, 153675);