Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D9×AΣL(1,𝔽16) |
| Fitting | C9×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C9 ⋊ C2×AΣL(1,𝔽16) |
657 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30140);