Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#85489 |
| Fitting | C23×C3×D4 ⋊ D3 |
766 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#85489, #72258598, C3×S4×AGL(1,ℤ/8), … |
| maximal normal subgroup of | #72258598, C3×S4×AGL(1,ℤ/8), D3×#85489 |
| maximal quotient of | A4×#85489 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156784);