Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×A4×C4⋊C4 |
| unambiguous semidirect product | (C22×D3×C4⋊C4)⋊C3 |
| Fitting | C22×C3×C4⋊C4 ⋊ C2×C3 |
1162 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 147 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, 157176);