Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | M32×#157 |
| Fitting | C32×M32 ⋊ C4 |
| Sylow | C32 ⋊ C4×M32 |
286 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | M32×PSU(3,𝔽2), M32×AGL(1,𝔽9), #72252847, … |
| maximal normal subgroup of | M32×PSU(3,𝔽2), M32×AGL(1,𝔽9), #72252847, … |
| maximal quotient of | #72252886 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 29866);