Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
| direct product | D8×C3⋊S4 |
| Fitting | C22×C3×D8 ⋊ D3 |
826 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×C3⋊S4, D8×A4⋊S4, D3×D8×S4, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×C3⋊S4, D3×D8×S4, #72274478 |
| maximal quotient of | D8×A4⋊S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157016);