Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | M16×C3⋊S4 |
| Fitting | C22×C3×M16 ⋊ D3 |
730 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | M16×A4⋊S4, AGL(1,ℤ/8)×C3⋊S4, D3×M16×S4, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×C3⋊S4, D3×M16×S4, #72274510 |
| maximal quotient of | M16×A4⋊S4, #97×C3⋊S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157001);