Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D3×#5417 |
| Fitting | C22×C3×Q8 ⋊ C2×D3 |
690 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#85460, D3×SD16×S4, D3×#85513, … |
| maximal normal subgroup of | D3×#85460, D3×SD16×S4, D3×#85513 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156189);