Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | A4×#893 |
| unambiguous semidirect product | (C22×#893)⋊C3 |
| Fitting | C22×C3×C4⋊C4 ⋊ C2×C3 |
1182 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157178);