Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×AGL(1,𝔽9) |
| Fitting | C32×C22⋊C4 ⋊ C8 |
| Sylow | C32 ⋊ C8×C22⋊C4 |
450 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 119 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 | C22⋊C4×AΓL(1,𝔽9), #120×AGL(1,𝔽9), #72220547, … |
| maximal normal subgroup of | C22⋊C4×AΓL(1,𝔽9), #120×AGL(1,𝔽9), #72220547, … |
| maximal quotient of | #72220584, #99×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17669);