Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×AΓL(1,𝔽9) |
| Fitting | C32×Q8 ⋊ SD16 |
| Sylow | C32 ⋊ Q8×SD16 |
448 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | Q8×AGL(2,𝔽3), SD16×AΓL(1,𝔽9), #41×AΓL(1,𝔽9), … |
| maximal normal subgroup of | SD16×AΓL(1,𝔽9), #41×AΓL(1,𝔽9), SL(2,𝔽3)×AΓL(1,𝔽9) |
| maximal quotient of | PSU(3,𝔽2)×AΓL(1,𝔽9), C4⋊C4×AΓL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 131234);