Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D3×A4×Q16 |
| unambiguous semidirect product | (C22×D3×Q16)⋊C3 |
| Fitting | C22×C3×Q16 ⋊ C2×C3 |
706 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157338);